[{"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"citation":{"chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000.","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","apa":"Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2000","ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 2024;34(1B):1623-1662. doi:10.1214/23-AAP2000"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["2208.12206"]},"author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"orcid":"0000-0003-2625-495X","full_name":"McKenna, Benjamin","last_name":"McKenna","id":"b0cc634c-d549-11ee-96c8-87338c7ad808","first_name":"Benjamin"}],"title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","acknowledgement":"The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation.","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","year":"2024","publication":"Annals of Applied Probability","day":"01","page":"1623-1662","date_created":"2024-02-25T23:00:56Z","doi":"10.1214/23-AAP2000","date_published":"2024-02-01T00:00:00Z","_id":"15025","type":"journal_article","article_type":"original","status":"public","date_updated":"2024-02-27T08:29:05Z","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2208.12206"}],"scopus_import":"1","intvolume":" 34","month":"02","publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"1B","volume":34},{"status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"11741","department":[{"_id":"LaEr"}],"file_date_updated":"2023-08-14T12:47:32Z","ddc":["510"],"date_updated":"2023-08-14T12:48:09Z","month":"04","intvolume":" 185","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.","lang":"eng"}],"volume":185,"license":"https://creativecommons.org/licenses/by/4.0/","file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"b9247827dae5544d1d19c37abe547abc","file_id":"14054","success":1,"date_updated":"2023-08-14T12:47:32Z","file_size":782278,"creator":"dernst","date_created":"2023-08-14T12:47:32Z","file_name":"2023_ProbabilityTheory_Cipolloni.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"publication_status":"published","title":"Quenched universality for deformed Wigner matrices","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer Nature, 2023. https://doi.org/10.1007/s00440-022-01156-7.","ama":"Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 2023;185:1183–1218. doi:10.1007/s00440-022-01156-7","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-022-01156-7","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” Probability Theory and Related Fields, vol. 185. Springer Nature, pp. 1183–1218, 2023.","mla":"Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:10.1007/s00440-022-01156-7."},"quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","doi":"10.1007/s00440-022-01156-7","date_published":"2023-04-01T00:00:00Z","date_created":"2022-08-07T22:02:00Z","page":"1183–1218","day":"01","publication":"Probability Theory and Related Fields","isi":1,"has_accepted_license":"1","year":"2023"},{"acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","publisher":"Wiley","quality_controlled":"1","oa":1,"day":"01","publication":"Communications on Pure and Applied Mathematics","has_accepted_license":"1","isi":1,"year":"2023","doi":"10.1002/cpa.22028","date_published":"2023-05-01T00:00:00Z","date_created":"2021-12-05T23:01:41Z","page":"946-1034","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 2023;76(5):946-1034. doi:10.1002/cpa.22028","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22028","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:10.1002/cpa.22028.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics. Wiley, 2023. https://doi.org/10.1002/cpa.22028."},"title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1912.04100"],"isi":["000724652500001"]},"article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. "}],"month":"05","intvolume":" 76","scopus_import":"1","file":[{"file_name":"2023_CommPureMathematics_Cipolloni.pdf","date_created":"2023-10-04T09:21:48Z","file_size":803440,"date_updated":"2023-10-04T09:21:48Z","creator":"dernst","success":1,"file_id":"14388","checksum":"8346bc2642afb4ccb7f38979f41df5d9","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"publication_status":"published","volume":76,"issue":"5","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","ec_funded":1,"_id":"10405","status":"public","article_type":"original","type":"journal_article","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"ddc":["510"],"date_updated":"2023-10-04T09:22:55Z","file_date_updated":"2023-10-04T09:21:48Z","department":[{"_id":"LaEr"}]},{"date_updated":"2023-10-04T10:21:07Z","department":[{"_id":"LaEr"}],"_id":"12707","article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"issn":["1350-7265"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":29,"issue":"2","abstract":[{"text":"We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"scopus_import":"1","intvolume":" 29","month":"05","citation":{"short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","ieee":"L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” Bernoulli, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.","ama":"Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 2023;29(2):1063-1079. doi:10.3150/22-BEJ1490","apa":"Erdös, L., & Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/22-BEJ1490","mla":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” Bernoulli, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:10.3150/22-BEJ1490.","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","chicago":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2023. https://doi.org/10.3150/22-BEJ1490."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"isi":["000947270100008"],"arxiv":["2112.12093 "]},"author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","last_name":"Xu","orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan"}],"title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"year":"2023","isi":1,"publication":"Bernoulli","day":"01","page":"1063-1079","date_created":"2023-03-05T23:01:05Z","date_published":"2023-05-01T00:00:00Z","doi":"10.3150/22-BEJ1490","oa":1,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","quality_controlled":"1"},{"title":"On the spectral form factor for random matrices","external_id":{"isi":["000957343500001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04692-y.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. Communications in Mathematical Physics. 2023;401:1665-1700. doi:10.1007/s00220-023-04692-y","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). On the spectral form factor for random matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04692-y","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” Communications in Mathematical Physics, vol. 401. Springer Nature, pp. 1665–1700, 2023.","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” Communications in Mathematical Physics, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:10.1007/s00220-023-04692-y."},"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"date_created":"2023-04-02T22:01:11Z","date_published":"2023-07-01T00:00:00Z","doi":"10.1007/s00220-023-04692-y","page":"1665-1700","publication":"Communications in Mathematical Physics","day":"01","year":"2023","has_accepted_license":"1","isi":1,"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","department":[{"_id":"LaEr"}],"file_date_updated":"2023-10-04T12:09:18Z","ddc":["510"],"date_updated":"2023-10-04T12:10:31Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"12792","ec_funded":1,"volume":401,"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"72057940f76654050ca84a221f21786c","file_id":"14397","creator":"dernst","file_size":859967,"date_updated":"2023-10-04T12:09:18Z","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_created":"2023-10-04T12:09:18Z"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"intvolume":" 401","month":"07","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics."}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-10-09T07:19:01Z","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2023. https://doi.org/10.1007/s00440-023-01229-1.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields.","mla":"Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2023, doi:10.1007/s00440-023-01229-1.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2023.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2023).","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 2023. doi:10.1007/s00440-023-01229-1"},"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","department":[{"_id":"LaEr"}],"article_processing_charge":"No","external_id":{"arxiv":["2210.12060"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"_id":"14408","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication":"Probability Theory and Related Fields","day":"28","publication_status":"epub_ahead","year":"2023","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"date_created":"2023-10-08T22:01:17Z","date_published":"2023-09-28T00:00:00Z","doi":"10.1007/s00440-023-01229-1","acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.","oa_version":"Preprint","abstract":[{"text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:10.1214/23-ECP516.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 2023;28:1-13. doi:10.1214/23-ECP516","apa":"Dubach, G., & Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP516","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP516.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"volume":28,"ec_funded":1,"publication_identifier":{"eissn":["1083-589X"]},"publication_status":"published","file":[{"date_created":"2023-02-27T09:43:27Z","file_name":"2023_ElectCommProbability_Dubach.pdf","date_updated":"2023-02-27T09:43:27Z","file_size":479105,"creator":"dernst","file_id":"12692","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"02","intvolume":" 28","abstract":[{"lang":"eng","text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices."}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file_date_updated":"2023-02-27T09:43:27Z","date_updated":"2023-10-17T12:48:10Z","ddc":["510"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"12683"},{"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","acknowledgement":"The second author is partially funded by the ERC Advanced Grant “RMTBEYOND” No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","date_created":"2023-03-26T22:01:08Z","date_published":"2023-02-01T00:00:00Z","doi":"10.1214/22-AAP1820","page":"447-489","publication":"Annals of Applied Probability","day":"01","year":"2023","isi":1,"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"title":"Functional central limit theorems for Wigner matrices","article_processing_charge":"No","external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AAP1820.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AAP1820","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 2023;33(1):447-489. doi:10.1214/22-AAP1820","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.","mla":"Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:10.1214/22-AAP1820."},"intvolume":" 33","month":"02","main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"ec_funded":1,"issue":"1","volume":33,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"status":"public","type":"journal_article","article_type":"original","_id":"12761","department":[{"_id":"LaEr"}],"date_updated":"2023-10-17T12:48:52Z"},{"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"publication_status":"epub_ahead","month":"10","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1142/S0129055X2360005X","open_access":"1"}],"oa_version":"Published Version","abstract":[{"text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"date_updated":"2023-11-20T10:04:38Z","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"14542","doi":"10.1142/s0129055x2360005x","date_published":"2023-10-31T00:00:00Z","date_created":"2023-11-15T23:48:14Z","day":"31","publication":"Reviews in Mathematical Physics","has_accepted_license":"1","year":"2023","quality_controlled":"1","publisher":"World Scientific Publishing","oa":1,"acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","title":"Universality in low-dimensional BCS theory","author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Lauritsen","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"},{"first_name":"Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","last_name":"Roos","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara"}],"external_id":{"arxiv":["2301.05621"]},"article_processing_charge":"Yes (in subscription journal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Henheik, S. J., Lauritsen, A. B., & Roos, B. (2023). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2023. doi:10.1142/s0129055x2360005x","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics. World Scientific Publishing, 2023.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, 2360005, World Scientific Publishing, 2023, doi:10.1142/s0129055x2360005x.","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005.","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2023. https://doi.org/10.1142/s0129055x2360005x."},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"article_number":"2360005 "},{"abstract":[{"lang":"eng","text":"For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. "},{"text":"On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.","lang":"fre"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.11382","open_access":"1"}],"month":"11","intvolume":" 59","publication_identifier":{"issn":["0246-0203"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":59,"issue":"4","ec_funded":1,"_id":"14667","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-12-11T12:36:56Z","department":[{"_id":"LaEr"}],"acknowledgement":"The first author was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated editor for carefully reading this paper and providing helpful comments that improved the quality of the article. Also the authors would like to thank Peter Forrester for pointing out the reference [12] that was absent in the previous version of the manuscript.","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"year":"2023","day":"01","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","page":"2083-2105","date_published":"2023-11-01T00:00:00Z","doi":"10.1214/22-AIHP1304","date_created":"2023-12-10T23:01:00Z","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"citation":{"ieee":"L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105.","apa":"Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304","ama":"Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105. doi:10.1214/22-AIHP1304","mla":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.","ista":"Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.","chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang","last_name":"Ji"}],"external_id":{"arxiv":["2112.11382"]},"article_processing_charge":"No","title":"Functional CLT for non-Hermitian random matrices"},{"_id":"13317","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["510","530"],"date_updated":"2023-12-13T11:38:44Z","file_date_updated":"2023-07-31T07:49:31Z","department":[{"_id":"LaEr"}],"oa_version":"Published Version","abstract":[{"text":"We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction.","lang":"eng"}],"intvolume":" 190","month":"07","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"file_name":"2023_JourStatPhysics_Sugimoto.pdf","date_created":"2023-07-31T07:49:31Z","creator":"dernst","file_size":612755,"date_updated":"2023-07-31T07:49:31Z","success":1,"file_id":"13325","checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"ec_funded":1,"volume":190,"issue":"7","article_number":"128","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” Journal of Statistical Physics. Springer Nature, 2023. https://doi.org/10.1007/s10955-023-03132-4.","ista":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128.","mla":"Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” Journal of Statistical Physics, vol. 190, no. 7, 128, Springer Nature, 2023, doi:10.1007/s10955-023-03132-4.","apa":"Sugimoto, S., Henheik, S. J., Riabov, V., & Erdös, L. (2023). Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-023-03132-4","ama":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 2023;190(7). doi:10.1007/s10955-023-03132-4","short":"S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023).","ieee":"S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” Journal of Statistical Physics, vol. 190, no. 7. Springer Nature, 2023."},"title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","article_processing_charge":"Yes (in subscription journal)","external_id":{"arxiv":["2304.04213"],"isi":["001035677200002"]},"author":[{"first_name":"Shoki","last_name":"Sugimoto","full_name":"Sugimoto, Shoki"},{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Riabov","full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"acknowledgement":"LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond” No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The University of Tokyo.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"Journal of Statistical Physics","day":"21","year":"2023","has_accepted_license":"1","isi":1,"date_created":"2023-07-30T22:01:02Z","doi":"10.1007/s10955-023-03132-4","date_published":"2023-07-21T00:00:00Z"},{"date_created":"2023-08-06T22:01:13Z","date_published":"2023-07-26T00:00:00Z","doi":"10.1007/s10959-023-01275-4","year":"2023","isi":1,"has_accepted_license":"1","publication":"Journal of Theoretical Probability","day":"26","oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"The first author thanks Yizhe Zhu for pointing out reference [30]. We thank David Renfrew for comments on an earlier draft. We thank the anonymous referee for a careful reading and helpful comments.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"author":[{"last_name":"Campbell","full_name":"Campbell, Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J"},{"full_name":"O’Rourke, Sean","last_name":"O’Rourke","first_name":"Sean"}],"title":"Spectrum of Lévy–Khintchine random laplacian matrices","citation":{"apa":"Campbell, A. J., & O’Rourke, S. (2023). Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. Springer Nature. https://doi.org/10.1007/s10959-023-01275-4","ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 2023. doi:10.1007/s10959-023-01275-4","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” Journal of Theoretical Probability. Springer Nature, 2023.","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability (2023).","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability, Springer Nature, 2023, doi:10.1007/s10959-023-01275-4.","ista":"Campbell AJ, O’Rourke S. 2023. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability. Springer Nature, 2023. https://doi.org/10.1007/s10959-023-01275-4."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s10959-023-01275-4"}],"scopus_import":"1","month":"07","abstract":[{"lang":"eng","text":"We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure."}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"date_updated":"2023-12-13T12:00:50Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"13975"},{"publication_identifier":{"eissn":["2050-5094"]},"publication_status":"published","file":[{"file_name":"2023_ForumMathematics_Cipolloni.pdf","date_created":"2023-09-20T11:09:35Z","creator":"dernst","file_size":852652,"date_updated":"2023-09-20T11:09:35Z","success":1,"checksum":"eb747420e6a88a7796fa934151957676","file_id":"14352","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"volume":11,"ec_funded":1,"abstract":[{"text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"08","intvolume":" 11","date_updated":"2023-12-13T12:24:23Z","ddc":["510"],"file_date_updated":"2023-09-20T11:09:35Z","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"_id":"14343","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","has_accepted_license":"1","isi":1,"year":"2023","day":"23","publication":"Forum of Mathematics, Sigma","doi":"10.1017/fms.2023.70","date_published":"2023-08-23T00:00:00Z","date_created":"2023-09-17T22:01:09Z","acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.","quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.70.","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.70","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.70","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 11, e74, Cambridge University Press, 2023, doi:10.1017/fms.2023.70."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","first_name":"Oleksii"}],"article_processing_charge":"Yes","external_id":{"isi":["001051980200001"],"arxiv":["2301.05181"]},"title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","article_number":"e74","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}]},{"acknowledgement":"J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331.","oa":1,"publisher":"IOP Publishing","quality_controlled":"1","publication":"Journal of Physics A: Mathematical and Theoretical","day":"11","year":"2023","has_accepted_license":"1","isi":1,"date_created":"2023-10-12T12:42:53Z","date_published":"2023-10-11T00:00:00Z","doi":"10.1088/1751-8121/acfe62","article_number":"445201","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point source,” Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 44. IOP Publishing, 2023.","short":"S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical 56 (2023).","ama":"Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 2023;56(44). doi:10.1088/1751-8121/acfe62","apa":"Henheik, S. J., & Tumulka, R. (2023). Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/acfe62","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:10.1088/1751-8121/acfe62.","ista":"Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2023. https://doi.org/10.1088/1751-8121/acfe62."},"title":"Creation rate of Dirac particles at a point source","external_id":{"arxiv":["2211.16606"],"isi":["001080908000001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\\in\\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\\psi_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission)."}],"intvolume":" 56","month":"10","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2023-10-16T07:07:24Z","file_size":721399,"date_created":"2023-10-16T07:07:24Z","file_name":"2023_JourPhysics_Henheik.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"5b68de147dd4c608b71a6e0e844d2ce9","file_id":"14429","success":1}],"publication_status":"published","publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"ec_funded":1,"issue":"44","volume":56,"_id":"14421","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2023-12-13T13:01:25Z","file_date_updated":"2023-10-16T07:07:24Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. The Annals of Applied Probability. 2023;33(4):2981-3009. doi:10.1214/22-aap1882","apa":"Ding, X., & Ji, H. C. (2023). Local laws for multiplication of random matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1882","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” The Annals of Applied Probability, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:10.1214/22-aap1882.","ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1882."},"title":"Local laws for multiplication of random matrices","external_id":{"arxiv":["2010.16083"]},"article_processing_charge":"No","author":[{"first_name":"Xiucai","last_name":"Ding","full_name":"Ding, Xiucai"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang","full_name":"Ji, Hong Chang","last_name":"Ji"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication":"The Annals of Applied Probability","day":"01","year":"2023","date_created":"2024-01-08T13:03:18Z","date_published":"2023-08-01T00:00:00Z","doi":"10.1214/22-aap1882","page":"2981-3009","acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","date_updated":"2024-01-09T08:16:41Z","department":[{"_id":"LaEr"}],"_id":"14750","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"ec_funded":1,"volume":33,"issue":"4","oa_version":"Preprint","abstract":[{"text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. ","lang":"eng"}],"intvolume":" 33","month":"08","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2010.16083","open_access":"1"}],"scopus_import":"1"},{"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","article_processing_charge":"No","external_id":{"arxiv":["2108.02728"],"isi":["000946432400021"]},"author":[{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"},{"full_name":"Xu, Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Schnelli, K., & Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1826","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 2023;33(1):677-725. doi:10.1214/22-aap1826","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” The Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:10.1214/22-aap1826.","ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1826."},"oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","date_created":"2024-01-10T09:23:31Z","doi":"10.1214/22-aap1826","date_published":"2023-02-01T00:00:00Z","page":"677-725","publication":"The Annals of Applied Probability","day":"01","year":"2023","isi":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"status":"public","type":"journal_article","article_type":"original","_id":"14775","department":[{"_id":"LaEr"}],"date_updated":"2024-01-10T13:31:46Z","intvolume":" 33","month":"02","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.02728","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble.","lang":"eng"}],"ec_funded":1,"volume":33,"issue":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1050-5164"]}},{"day":"01","publication":"Stochastic Processes and their Applications","has_accepted_license":"1","isi":1,"year":"2023","doi":"10.1016/j.spa.2023.05.009","date_published":"2023-09-01T00:00:00Z","date_created":"2024-01-10T09:29:25Z","page":"25-60","acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","quality_controlled":"1","publisher":"Elsevier","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications. Elsevier, 2023. https://doi.org/10.1016/j.spa.2023.05.009.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” Stochastic Processes and their Applications, vol. 163. Elsevier, pp. 25–60, 2023.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","apa":"Ding, X., & Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2023.05.009","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 2023;163:25-60. doi:10.1016/j.spa.2023.05.009","mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications, vol. 163, Elsevier, 2023, pp. 25–60, doi:10.1016/j.spa.2023.05.009."},"title":"Spiked multiplicative random matrices and principal components","author":[{"last_name":"Ding","full_name":"Ding, Xiucai","first_name":"Xiucai"},{"last_name":"Ji","full_name":"Ji, Hong Chang","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"article_processing_charge":"Yes (in subscription journal)","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"file":[{"checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","file_id":"14806","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2024-01-16T08:47:31Z","file_name":"2023_StochasticProcAppl_Ding.pdf","creator":"dernst","date_updated":"2024-01-16T08:47:31Z","file_size":1870349}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1879-209X"],"issn":["0304-4149"]},"publication_status":"published","volume":163,"ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.","lang":"eng"}],"month":"09","intvolume":" 163","ddc":["510"],"date_updated":"2024-01-16T08:49:51Z","department":[{"_id":"LaEr"}],"file_date_updated":"2024-01-16T08:47:31Z","_id":"14780","status":"public","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"}},{"type":"journal_article","article_type":"original","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"status":"public","_id":"14849","department":[{"_id":"LaEr"}],"date_updated":"2024-01-23T10:56:30Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.04448","open_access":"1"}],"intvolume":" 51","month":"11","abstract":[{"lang":"eng","text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal."}],"oa_version":"Preprint","ec_funded":1,"issue":"6","volume":51,"publication_status":"published","publication_identifier":{"issn":["0091-1798"]},"language":[{"iso":"eng"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"external_id":{"arxiv":["2206.04448"]},"article_processing_charge":"No","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan"}],"title":"On the rightmost eigenvalue of non-Hermitian random matrices","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-aop1643.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” The Annals of Probability, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-aop1643","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 2023;51(6):2192-2242. doi:10.1214/23-aop1643","mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:10.1214/23-aop1643."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","page":"2192-2242","date_created":"2024-01-22T08:08:41Z","date_published":"2023-11-01T00:00:00Z","doi":"10.1214/23-aop1643","year":"2023","publication":"The Annals of Probability","day":"01"},{"month":"01","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.01712","open_access":"1"}],"oa_version":"Preprint","acknowledgement":"Supported by the ERC Advanced Grant ”RMTBeyond” No. 101020331","abstract":[{"text":"We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,\\zeta)$ and a general class of related quantities involving two resolvents\r\nat nearby spectral parameters. ","lang":"eng"}],"date_published":"2023-01-04T00:00:00Z","doi":"10.48550/arXiv.2301.01712","ec_funded":1,"date_created":"2024-03-20T09:41:04Z","day":"04","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","year":"2023","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"status":"public","type":"preprint","article_number":"2301.01712","_id":"15128","title":"Mesoscopic eigenvalue statistics for Wigner-type matrices","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"author":[{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr","last_name":"Riabov","full_name":"Riabov, Volodymyr"}],"article_processing_charge":"No","external_id":{"arxiv":["2301.01712"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv, 2301.01712.","chicago":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2301.01712.","short":"V. Riabov, ArXiv (n.d.).","ieee":"V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” arXiv. .","apa":"Riabov, V. (n.d.). Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. https://doi.org/10.48550/arXiv.2301.01712","ama":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. doi:10.48550/arXiv.2301.01712","mla":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, 2301.01712, doi:10.48550/arXiv.2301.01712."},"date_updated":"2024-03-25T12:48:20Z"},{"author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"article_processing_charge":"No","external_id":{"arxiv":["2105.13719"]},"title":"On the condition number of the shifted real Ginibre ensemble","citation":{"mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487. doi:10.1137/21m1424408","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","oa":1,"page":"1469-1487","doi":"10.1137/21m1424408","date_published":"2022-07-01T00:00:00Z","date_created":"2023-01-12T12:12:38Z","year":"2022","day":"01","publication":"SIAM Journal on Matrix Analysis and Applications","article_type":"original","type":"journal_article","status":"public","keyword":["Analysis"],"_id":"12179","department":[{"_id":"LaEr"}],"date_updated":"2023-01-27T06:56:06Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"month":"07","intvolume":" 43","abstract":[{"lang":"eng","text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146]."}],"oa_version":"Preprint","issue":"3","volume":43,"publication_identifier":{"eissn":["1095-7162"],"issn":["0895-4798"]},"publication_status":"published","language":[{"iso":"eng"}]},{"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_number":"011901","title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","article_processing_charge":"No","external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0051632","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” Journal of Mathematical Physics, vol. 63, no. 1. AIP Publishing, 2022.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632."},"oa":1,"publisher":"AIP Publishing","quality_controlled":"1","acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","date_created":"2022-01-03T12:19:48Z","doi":"10.1063/5.0051632","date_published":"2022-01-03T00:00:00Z","publication":"Journal of Mathematical Physics","day":"03","year":"2022","isi":1,"keyword":["mathematical physics","statistical and nonlinear physics"],"status":"public","type":"journal_article","article_type":"original","_id":"10600","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_updated":"2023-08-02T13:44:32Z","intvolume":" 63","month":"01","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.","lang":"eng"}],"ec_funded":1,"issue":"1","volume":63,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]}},{"publication_status":"published","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","date_updated":"2022-01-19T09:41:14Z","file_size":357547,"date_created":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"10647","checksum":"7e8e69b76e892c305071a4736131fe18","success":1}],"ec_funded":1,"volume":112,"issue":"1","abstract":[{"lang":"eng","text":"Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences."}],"oa_version":"Published Version","intvolume":" 112","month":"01","date_updated":"2023-08-02T13:57:02Z","ddc":["530"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:41:14Z","_id":"10642","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","keyword":["mathematical physics","statistical and nonlinear physics"],"status":"public","year":"2022","has_accepted_license":"1","isi":1,"publication":"Letters in Mathematical Physics","day":"18","date_created":"2022-01-18T16:18:25Z","date_published":"2022-01-18T00:00:00Z","doi":"10.1007/s11005-021-01494-y","acknowledgement":"J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","citation":{"chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y.","ista":"Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9.","mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y.","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” Letters in Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022.","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y","apa":"Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000744930400001"],"arxiv":["2106.13780"]},"article_processing_charge":"No","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}],"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","article_number":"9","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}]},{"date_updated":"2023-08-02T13:53:11Z","ddc":["510"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:27:43Z","_id":"10643","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"status":"public","publication_status":"published","publication_identifier":{"eissn":["2050-5094"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","success":1,"creator":"cchlebak","date_updated":"2022-01-19T09:27:43Z","file_size":705323,"date_created":"2022-01-19T09:27:43Z","file_name":"2022_ForumMathSigma_Henheik.pdf"}],"ec_funded":1,"volume":10,"abstract":[{"text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n","lang":"eng"}],"oa_version":"Published Version","intvolume":" 10","month":"01","citation":{"mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","article_number":"e4","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"year":"2022","has_accepted_license":"1","isi":1,"publication":"Forum of Mathematics, Sigma","day":"18","date_created":"2022-01-18T16:18:51Z","doi":"10.1017/fms.2021.80","date_published":"2022-01-18T00:00:00Z","acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press"},{"year":"2022","isi":1,"has_accepted_license":"1","publication":"Mathematical Physics, Analysis and Geometry","day":"11","date_created":"2022-01-13T15:40:53Z","date_published":"2022-01-11T00:00:00Z","doi":"10.1007/s11040-021-09415-0","acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","citation":{"chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0.","ama":"Henheik SJ. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000741387600001"],"arxiv":["2106.02015"]},"author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"title":"The BCS critical temperature at high density","article_number":"3","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"language":[{"iso":"eng"}],"file":[{"success":1,"file_id":"10624","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","date_created":"2022-01-14T07:27:45Z","creator":"cchlebak","file_size":505804,"date_updated":"2022-01-14T07:27:45Z"}],"ec_funded":1,"issue":"1","volume":25,"abstract":[{"text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 25","month":"01","date_updated":"2023-08-02T13:51:52Z","ddc":["514"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-14T07:27:45Z","_id":"10623","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","keyword":["geometry and topology","mathematical physics"],"status":"public"},{"article_number":"109394","citation":{"mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis, vol. 282, no. 8, 109394, Elsevier, 2022, doi:10.1016/j.jfa.2022.109394.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. Journal of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109394.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]},"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Thermalisation for Wigner matrices","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","oa":1,"publisher":"Elsevier","quality_controlled":"1","year":"2022","has_accepted_license":"1","isi":1,"publication":"Journal of Functional Analysis","day":"15","date_created":"2022-02-06T23:01:30Z","doi":"10.1016/j.jfa.2022.109394","date_published":"2022-04-15T00:00:00Z","_id":"10732","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","date_updated":"2023-08-02T14:12:35Z","ddc":["500"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-07-29T07:22:08Z","abstract":[{"lang":"eng","text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 282","month":"04","publication_status":"published","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"b75fdad606ab507dc61109e0907d86c0","file_id":"11690","file_size":652573,"date_updated":"2022-07-29T07:22:08Z","creator":"dernst","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","date_created":"2022-07-29T07:22:08Z"}],"issue":"8","volume":282},{"citation":{"ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications. World Scientific, 2022. https://doi.org/10.1142/s2010326322500368.","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World Scientific, 2022.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:10.1142/s2010326322500368."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Reker","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana"}],"external_id":{"arxiv":["2103.03906"],"isi":["000848873800001"]},"article_processing_charge":"No","title":"On the operator norm of a Hermitian random matrix with correlated entries","article_number":"2250036","isi":1,"year":"2022","day":"01","publication":"Random Matrices: Theory and Applications","date_published":"2022-10-01T00:00:00Z","doi":"10.1142/s2010326322500368","date_created":"2022-04-08T07:11:12Z","publisher":"World Scientific","quality_controlled":"1","oa":1,"date_updated":"2023-08-03T06:32:22Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"_id":"11135","type":"journal_article","article_type":"original","status":"public","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":11,"issue":"4","abstract":[{"lang":"eng","text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"month":"10","intvolume":" 11"},{"acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"day":"01","publication":"Communications in Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2022","doi":"10.1007/s00220-022-04377-y","date_published":"2022-07-01T00:00:00Z","date_created":"2022-04-24T22:01:44Z","page":"839-907","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 2022;393:839-907. doi:10.1007/s00220-022-04377-y","apa":"Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” Communications in Mathematical Physics, vol. 393. Springer Nature, pp. 839–907, 2022.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y."},"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","author":[{"first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan"}],"article_processing_charge":"No","external_id":{"arxiv":["2102.04330"],"isi":["000782737200001"]},"oa_version":"Published Version","abstract":[{"text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles.","lang":"eng"}],"month":"07","intvolume":" 393","scopus_import":"1","file":[{"checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_id":"11726","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2022-08-05T06:01:13Z","file_name":"2022_CommunMathPhys_Schnelli.pdf","creator":"dernst","date_updated":"2022-08-05T06:01:13Z","file_size":1141462}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","volume":393,"ec_funded":1,"_id":"11332","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-08-03T06:34:24Z","department":[{"_id":"LaEr"}],"file_date_updated":"2022-08-05T06:01:13Z"},{"author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","citation":{"mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552.","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","page":"984-1012","doi":"10.1214/21-AOP1552","date_published":"2022-05-01T00:00:00Z","date_created":"2022-05-29T22:01:53Z","isi":1,"year":"2022","day":"01","publication":"Annals of Probability","type":"journal_article","article_type":"original","status":"public","_id":"11418","department":[{"_id":"LaEr"}],"date_updated":"2023-08-03T07:16:53Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"month":"05","intvolume":" 50","abstract":[{"lang":"eng","text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"oa_version":"Preprint","issue":"3","volume":50,"publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"publication_status":"published","language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","file":[{"file_id":"12327","checksum":"5150287295e0ce4f12462c990744d65d","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2023-01-20T11:58:59Z","file_name":"2022_JourMathPhysics_Henheik.pdf","date_updated":"2023-01-20T11:58:59Z","file_size":5436804,"creator":"dernst"}],"language":[{"iso":"eng"}],"issue":"12","volume":63,"ec_funded":1,"abstract":[{"lang":"eng","text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential."}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 63","date_updated":"2023-08-03T14:12:01Z","ddc":["510"],"file_date_updated":"2023-01-20T11:58:59Z","department":[{"_id":"LaEr"}],"_id":"12110","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Journal of Mathematical Physics","date_published":"2022-12-01T00:00:00Z","doi":"10.1063/5.0104675","date_created":"2023-01-08T23:00:53Z","acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","quality_controlled":"1","publisher":"AIP Publishing","oa":1,"citation":{"ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104675.","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0104675","apa":"Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104675","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}],"external_id":{"isi":["000900748900002"]},"article_processing_charge":"No","title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","article_number":"122302","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}]},{"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_number":"e96","title":"Rank-uniform local law for Wigner matrices","article_processing_charge":"No","external_id":{"isi":["000873719200001"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022)."},"oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","date_created":"2023-01-12T12:07:30Z","date_published":"2022-10-27T00:00:00Z","doi":"10.1017/fms.2022.86","publication":"Forum of Mathematics, Sigma","day":"27","year":"2022","has_accepted_license":"1","isi":1,"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"12148","file_date_updated":"2023-01-24T10:02:40Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-04T09:00:35Z","intvolume":" 10","month":"10","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"ec_funded":1,"volume":10,"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400","creator":"dernst","file_size":817089,"date_updated":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","date_created":"2023-01-24T10:02:40Z"}],"publication_status":"published","publication_identifier":{"issn":["2050-5094"]}},{"article_number":"121101","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"citation":{"ieee":"S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","ama":"Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0123441","apa":"Henheik, S. J., & Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0123441","mla":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:10.1063/5.0123441.","ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","chicago":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0123441."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Tom","full_name":"Wessel, Tom","last_name":"Wessel"}],"article_processing_charge":"No","external_id":{"arxiv":["2208.12220"],"isi":["000905776200001"]},"title":"On adiabatic theory for extended fermionic lattice systems","acknowledgement":"It is a pleasure to thank Stefan Teufel for numerous interesting discussions, fruitful collaboration, and many helpful comments on an earlier version of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges financial support from the DFG research unit FOR 5413 “Long-range interacting quantum spin systems out of equilibrium: Experiment, Theory and Mathematics.\" ","publisher":"AIP Publishing","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Journal of Mathematical Physics","doi":"10.1063/5.0123441","date_published":"2022-12-01T00:00:00Z","date_created":"2023-01-15T23:00:52Z","_id":"12184","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-04T09:14:57Z","ddc":["510"],"file_date_updated":"2023-01-27T07:10:52Z","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","text":"We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs."}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 63","publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"213b93750080460718c050e4967cfdb4","file_id":"12410","file_size":5251092,"date_updated":"2023-01-27T07:10:52Z","creator":"dernst","file_name":"2022_JourMathPhysics_Henheik2.pdf","date_created":"2023-01-27T07:10:52Z"}],"language":[{"iso":"eng"}],"volume":63,"issue":"12","ec_funded":1},{"citation":{"ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894. doi:10.1112/jlms.12676","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12676","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:10.1112/jlms.12676.","ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Gehér","full_name":"Gehér, György Pál","first_name":"György Pál"},{"last_name":"Titkos","full_name":"Titkos, Tamás","first_name":"Tamás"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"external_id":{"arxiv":["2102.02037"],"isi":["000854878500001"]},"article_processing_charge":"No","title":"The isometry group of Wasserstein spaces: The Hilbertian case","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"isi":1,"year":"2022","day":"18","publication":"Journal of the London Mathematical Society","page":"3865-3894","doi":"10.1112/jlms.12676","date_published":"2022-09-18T00:00:00Z","date_created":"2023-01-16T09:46:13Z","acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","publisher":"Wiley","quality_controlled":"1","oa":1,"date_updated":"2023-08-04T09:24:17Z","department":[{"_id":"LaEr"}],"_id":"12214","article_type":"original","type":"journal_article","status":"public","keyword":["General Mathematics"],"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":106,"issue":"4","ec_funded":1,"abstract":[{"text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. ","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2102.02037","open_access":"1"}],"month":"09","intvolume":" 106"},{"date_updated":"2023-08-04T09:33:52Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T11:06:47Z","_id":"12232","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"publication_status":"published","file":[{"checksum":"5582f059feeb2f63e2eb68197a34d7dc","file_id":"12424","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2023-01-27T11:06:47Z","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","creator":"dernst","date_updated":"2023-01-27T11:06:47Z","file_size":1333638}],"language":[{"iso":"eng"}],"issue":"11","volume":23,"abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"11","intvolume":" 23","citation":{"mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002. doi:10.1007/s00023-022-01188-8","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-022-01188-8","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000796323500001"]},"article_processing_charge":"No","title":"Density of small singular values of the shifted real Ginibre ensemble","has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Annales Henri Poincaré","page":"3981-4002","doi":"10.1007/s00023-022-01188-8","date_published":"2022-11-01T00:00:00Z","date_created":"2023-01-16T09:50:26Z","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","quality_controlled":"1","publisher":"Springer Nature","oa":1},{"volume":63,"issue":"10","ec_funded":1,"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"publication_status":"published","file":[{"date_created":"2023-01-30T08:01:10Z","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","creator":"dernst","date_updated":"2023-01-30T08:01:10Z","file_size":7356807,"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"10","intvolume":" 63","abstract":[{"text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ","lang":"eng"}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-30T08:01:10Z","date_updated":"2023-08-04T09:40:02Z","ddc":["510","530"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"_id":"12243","date_published":"2022-10-14T00:00:00Z","doi":"10.1063/5.0104290","date_created":"2023-01-16T09:52:58Z","isi":1,"has_accepted_license":"1","year":"2022","day":"14","publication":"Journal of Mathematical Physics","publisher":"AIP Publishing","quality_controlled":"1","oa":1,"acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"},{"first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"external_id":{"isi":["000869715800001"],"arxiv":["2206.04443"]},"article_processing_charge":"Yes (via OA deal)","title":"Directional extremal statistics for Ginibre eigenvalues","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104290","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:10.1063/5.0104290."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_number":"103303"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:10.1214/22-ejp838.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022."},"title":"Optimal multi-resolvent local laws for Wigner matrices","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"external_id":{"isi":["000910863700003"]},"article_processing_charge":"No","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"day":"12","publication":"Electronic Journal of Probability","isi":1,"has_accepted_license":"1","year":"2022","date_published":"2022-09-12T00:00:00Z","doi":"10.1214/22-ejp838","date_created":"2023-01-16T10:04:38Z","page":"1-38","acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"ddc":["510"],"date_updated":"2023-08-04T10:32:23Z","file_date_updated":"2023-01-30T11:59:21Z","department":[{"_id":"LaEr"}],"_id":"12290","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"bb647b48fbdb59361210e425c220cdcb","file_id":"12464","file_size":502149,"date_updated":"2023-01-30T11:59:21Z","creator":"dernst","file_name":"2022_ElecJournProbability_Cipolloni.pdf","date_created":"2023-01-30T11:59:21Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","volume":27,"ec_funded":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"month":"09","intvolume":" 27","scopus_import":"1"},{"article_number":"5","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9.","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9","apa":"Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9"},"title":"The BCS energy gap at high density","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000833007200002"]},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","oa":1,"publisher":"Springer Nature","quality_controlled":"1","publication":"Journal of Statistical Physics","day":"29","year":"2022","has_accepted_license":"1","isi":1,"date_created":"2022-08-05T11:36:56Z","date_published":"2022-07-29T00:00:00Z","doi":"10.1007/s10955-022-02965-9","_id":"11732","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","ddc":["530"],"date_updated":"2023-09-05T14:57:49Z","file_date_updated":"2022-08-08T07:36:34Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature."}],"intvolume":" 189","month":"07","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"file_id":"11746","checksum":"b398c4dbf65f71d417981d6e366427e9","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2022-08-08T07:36:34Z","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","creator":"dernst","date_updated":"2022-08-08T07:36:34Z","file_size":419563}],"publication_status":"published","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"ec_funded":1,"volume":189},{"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur."}],"intvolume":" 26","month":"09","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"checksum":"1c975afb31460277ce4d22b93538e5f9","file_id":"10288","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2021-11-15T10:10:17Z","file_name":"2021_ElecJournalProb_Dubach.pdf","creator":"cchlebak","date_updated":"2021-11-15T10:10:17Z","file_size":735940}],"publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"ec_funded":1,"volume":26,"_id":"10285","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["519"],"date_updated":"2021-11-15T10:48:46Z","department":[{"_id":"LaEr"}],"file_date_updated":"2021-11-15T10:10:17Z","acknowledgement":"We acknowledge partial support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would like to thank Paul Bourgade and László Erdős for many helpful comments.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Electronic Journal of Probability","day":"28","year":"2021","has_accepted_license":"1","date_created":"2021-11-14T23:01:25Z","date_published":"2021-09-28T00:00:00Z","doi":"10.1214/21-EJP686","article_number":"124","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP686.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","mla":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP686","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686"},"title":"On eigenvector statistics in the spherical and truncated unitary ensembles","article_processing_charge":"No","author":[{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137"}]},{"date_created":"2021-03-09T11:08:15Z","ec_funded":1,"doi":"10.48550/arXiv.2103.04817","date_published":"2021-03-08T00:00:00Z","year":"2021","publication_status":"submitted","language":[{"iso":"eng"}],"publication":"arXiv","day":"08","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"month":"03","abstract":[{"lang":"eng","text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals."}],"acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","oa_version":"Preprint","article_processing_charge":"No","external_id":{"arxiv":["2103.04817"]},"author":[{"last_name":"Arguin","full_name":"Arguin, Louis-Pierre","first_name":"Louis-Pierre"},{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach"},{"first_name":"Lisa","full_name":"Hartung, Lisa","last_name":"Hartung"}],"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","department":[{"_id":"LaEr"}],"citation":{"chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.04817.","ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817","apa":"Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” arXiv. .","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.)."},"date_updated":"2023-05-03T10:22:59Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"preprint","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"status":"public","_id":"9230","article_number":"2103.04817"},{"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics."}],"month":"03","main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"oa":1,"day":"21","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","year":"2021","date_published":"2021-03-21T00:00:00Z","doi":"10.48550/arXiv.2103.11389","related_material":{"record":[{"id":"9946","status":"public","relation":"other"}]},"ec_funded":1,"date_created":"2021-03-23T05:38:48Z","article_number":"2103.11389","_id":"9281","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"status":"public","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-05-03T10:26:45Z","citation":{"chicago":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389.","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.","ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv. doi:10.48550/arXiv.2103.11389","apa":"Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” arXiv. ."},"title":"Formal verification of Zagier's one-sentence proof","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"author":[{"last_name":"Dubach","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"},{"last_name":"Mühlböck","orcid":"0000-0003-1548-0177","full_name":"Mühlböck, Fabian","first_name":"Fabian","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425"}],"article_processing_charge":"No","external_id":{"arxiv":["2103.11389"]}},{"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","author":[{"last_name":"Pitrik","full_name":"Pitrik, József","first_name":"József"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"article_processing_charge":"No","external_id":{"arxiv":["2002.11678"],"isi":["000581730500011"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007","ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.","mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021, pp. 203–17, doi:10.1016/j.laa.2020.09.007.","ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007."},"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"},{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"date_published":"2021-01-15T00:00:00Z","doi":"10.1016/j.laa.2020.09.007","date_created":"2020-09-11T08:35:50Z","page":"203-217","day":"15","publication":"Linear Algebra and its Applications","isi":1,"year":"2021","quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T10:58:14Z","status":"public","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"type":"journal_article","article_type":"original","_id":"8373","volume":609,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0024-3795"]},"publication_status":"published","month":"01","intvolume":" 609","main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.","lang":"eng"}]},{"date_created":"2021-01-22T17:55:17Z","doi":"10.1016/j.aim.2021.107595","date_published":"2021-03-26T00:00:00Z","year":"2021","isi":1,"publication":"Advances in Mathematics","day":"26","oa":1,"publisher":"Elsevier","quality_controlled":"1","acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","external_id":{"isi":["000619676100035"],"arxiv":["1910.10447"]},"article_processing_charge":"No","author":[{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek"}],"title":"The metric property of the quantum Jensen-Shannon divergence","citation":{"chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.","ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595","short":"D. Virosztek, Advances in Mathematics 380 (2021).","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"}],"article_number":"107595","ec_funded":1,"volume":380,"issue":"3","publication_status":"published","publication_identifier":{"issn":["0001-8708"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1910.10447","open_access":"1"}],"intvolume":" 380","month":"03","abstract":[{"lang":"eng","text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space."}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-08-07T13:34:48Z","type":"journal_article","article_type":"original","keyword":["General Mathematics"],"status":"public","_id":"9036"},{"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness."}],"intvolume":" 26","month":"03","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_id":"9423","creator":"kschuh","file_size":865148,"date_updated":"2021-05-25T13:24:19Z","file_name":"2021_EJP_Cipolloni.pdf","date_created":"2021-05-25T13:24:19Z"}],"publication_status":"published","publication_identifier":{"eissn":["10836489"]},"ec_funded":1,"volume":26,"_id":"9412","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","ddc":["510"],"date_updated":"2023-08-08T13:39:19Z","department":[{"_id":"LaEr"}],"file_date_updated":"2021-05-25T13:24:19Z","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Electronic Journal of Probability","day":"23","year":"2021","has_accepted_license":"1","isi":1,"date_created":"2021-05-23T22:01:44Z","date_published":"2021-03-23T00:00:00Z","doi":"10.1214/21-EJP591","article_number":"24","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591.","ama":"Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP591","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","mla":"Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591."},"title":"Fluctuation around the circular law for random matrices with real entries","article_processing_charge":"No","external_id":{"isi":["000641855600001"],"arxiv":["2002.02438"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}]},{"publisher":"Cambridge University Press","quality_controlled":"1","oa":1,"acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","date_published":"2021-05-27T00:00:00Z","doi":"10.1017/fms.2021.38","date_created":"2021-06-13T22:01:33Z","has_accepted_license":"1","isi":1,"year":"2021","day":"27","publication":"Forum of Mathematics, Sigma","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"article_number":"e44","author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"external_id":{"arxiv":["2008.07061"],"isi":["000654960800001"]},"article_processing_charge":"No","title":"Equipartition principle for Wigner matrices","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.38.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.38","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","month":"05","intvolume":" 9","abstract":[{"lang":"eng","text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. "}],"oa_version":"Published Version","volume":9,"ec_funded":1,"publication_identifier":{"eissn":["20505094"]},"publication_status":"published","file":[{"date_created":"2021-06-15T14:40:45Z","file_name":"2021_ForumMath_Bao.pdf","creator":"cziletti","date_updated":"2021-06-15T14:40:45Z","file_size":483458,"checksum":"47c986578de132200d41e6d391905519","file_id":"9555","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"9550","file_date_updated":"2021-06-15T14:40:45Z","department":[{"_id":"LaEr"}],"date_updated":"2023-08-08T14:03:40Z","ddc":["510"]},{"abstract":[{"text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 22","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"publication_status":"published","file":[{"file_name":"2021_AnnHenriPoincare_Erdoes.pdf","date_created":"2022-05-12T12:50:27Z","creator":"dernst","file_size":1162454,"date_updated":"2022-05-12T12:50:27Z","success":1,"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","file_id":"11365","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"volume":22,"ec_funded":1,"_id":"9912","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-11T10:31:48Z","ddc":["510"],"file_date_updated":"2022-05-12T12:50:27Z","department":[{"_id":"LaEr"}],"acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Annales Henri Poincaré ","page":"4205–4269","doi":"10.1007/s00023-021-01085-6","date_published":"2021-12-01T00:00:00Z","date_created":"2021-08-15T22:01:29Z","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"citation":{"chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:10.1007/s00023-021-01085-6.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature, pp. 4205–4269, 2021.","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . Springer Nature. https://doi.org/10.1007/s00023-021-01085-6","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"},{"last_name":"Nemish","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy"}],"article_processing_charge":"Yes (in subscription journal)","external_id":{"isi":["000681531500001"],"arxiv":["1911.05112"]},"title":"Scattering in quantum dots via noncommutative rational functions"},{"volume":388,"issue":"2","publication_status":"published","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","date_updated":"2022-02-02T10:19:55Z","file_size":841426,"date_created":"2022-02-02T10:19:55Z","file_name":"2021_CommunMathPhys_Cipolloni.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"10715","checksum":"a2c7b6f5d23b5453cd70d1261272283b","success":1}],"scopus_import":"1","intvolume":" 388","month":"10","abstract":[{"lang":"eng","text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020)."}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file_date_updated":"2022-02-02T10:19:55Z","date_updated":"2023-08-14T10:29:49Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"10221","page":"1005–1048","date_created":"2021-11-07T23:01:25Z","doi":"10.1007/s00220-021-04239-z","date_published":"2021-10-29T00:00:00Z","year":"2021","has_accepted_license":"1","isi":1,"publication":"Communications in Mathematical Physics","day":"29","oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” Communications in Mathematical Physics, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04239-z","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048. doi:10.1007/s00220-021-04239-z","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"day":"25","year":"2021","has_accepted_license":"1","date_created":"2021-01-21T18:16:54Z","date_published":"2021-01-25T00:00:00Z","doi":"10.15479/AT:ISTA:9022","page":"380","acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","oa":1,"publisher":"Institute of Science and Technology Austria","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","apa":"Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022"},"title":"Fluctuations in the spectrum of random matrices","article_processing_charge":"No","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"}],"project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"},{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9043","checksum":"5a93658a5f19478372523ee232887e2b","success":1,"creator":"gcipollo","date_updated":"2021-01-25T14:19:03Z","file_size":4127796,"date_created":"2021-01-25T14:19:03Z","file_name":"thesis.pdf"},{"file_id":"9044","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","access_level":"closed","relation":"source_file","content_type":"application/zip","date_created":"2021-01-25T14:19:10Z","file_name":"Thesis_files.zip","creator":"gcipollo","date_updated":"2021-01-25T14:19:10Z","file_size":12775206}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.","lang":"eng"}],"month":"01","alternative_title":["ISTA Thesis"],"ddc":["510"],"date_updated":"2023-09-07T13:29:32Z","supervisor":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"file_date_updated":"2021-01-25T14:19:10Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"_id":"9022","status":"public","type":"dissertation"},{"citation":{"ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” Probability and Mathematical Physics, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221","ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1907.13631"]},"article_processing_charge":"No","author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"title":"Spectral radius of random matrices with independent entries","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"year":"2021","publication":"Probability and Mathematical Physics","day":"21","page":"221-280","date_created":"2024-02-18T23:01:03Z","doi":"10.2140/pmp.2021.2.221","date_published":"2021-05-21T00:00:00Z","acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","oa":1,"publisher":"Mathematical Sciences Publishers","quality_controlled":"1","date_updated":"2024-02-19T08:30:00Z","department":[{"_id":"LaEr"}],"_id":"15013","type":"journal_article","article_type":"original","status":"public","publication_status":"published","publication_identifier":{"eissn":["2690-1005"],"issn":["2690-0998"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"2","volume":2,"abstract":[{"lang":"eng","text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge."}],"oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"scopus_import":"1","intvolume":" 2","month":"05"},{"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385"}],"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"title":"Edge universality for non-Hermitian random matrices","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","quality_controlled":"1","oa":1,"date_published":"2021-02-01T00:00:00Z","doi":"10.1007/s00440-020-01003-7","date_created":"2020-10-04T22:01:37Z","has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Probability Theory and Related Fields","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"8601","department":[{"_id":"LaEr"}],"file_date_updated":"2020-10-05T14:53:40Z","date_updated":"2024-03-07T15:07:53Z","ddc":["510"],"scopus_import":"1","month":"02","abstract":[{"text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"publication_status":"published","file":[{"creator":"dernst","date_updated":"2020-10-05T14:53:40Z","file_size":497032,"date_created":"2020-10-05T14:53:40Z","file_name":"2020_ProbTheory_Cipolloni.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"611ae28d6055e1e298d53a57beb05ef4","file_id":"8612","success":1}],"language":[{"iso":"eng"}]},{"project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"author":[{"first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal","last_name":"Geher"},{"first_name":"Tamas","last_name":"Titkos","full_name":"Titkos, Tamas"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511"}],"article_processing_charge":"No","external_id":{"arxiv":["2002.00859"],"isi":["000551418100018"]},"title":"Isometric study of Wasserstein spaces - the real line","citation":{"ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 2020;373(8):5855-5883. doi:10.1090/tran/8113","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/8113","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” Transactions of the American Mathematical Society, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113.","ista":"Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"page":"5855-5883","date_published":"2020-08-01T00:00:00Z","doi":"10.1090/tran/8113","date_created":"2020-01-29T10:20:46Z","isi":1,"year":"2020","day":"01","publication":"Transactions of the American Mathematical Society","article_type":"original","type":"journal_article","status":"public","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"_id":"7389","department":[{"_id":"LaEr"}],"date_updated":"2023-08-17T14:31:03Z","ddc":["515"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"month":"08","intvolume":" 373","abstract":[{"lang":"eng","text":"Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R) is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R))."}],"oa_version":"Preprint","volume":373,"issue":"8","ec_funded":1,"publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"publication_status":"published","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00221236"],"eissn":["10960783"]},"ec_funded":1,"volume":278,"issue":"12","oa_version":"Preprint","abstract":[{"text":"We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have the same variance. We show that under certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory. We prove that these conditions hold for general homogeneous polynomials of degree two and for symmetrized products of independent matrices with i.i.d. entries, thus establishing the optimal bulk local law for these classes of ensembles. In particular, we generalize a similar result of Anderson for anticommutator. For more general polynomials our conditions are effectively checkable numerically.","lang":"eng"}],"intvolume":" 278","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"scopus_import":"1","date_updated":"2023-08-18T06:36:10Z","department":[{"_id":"LaEr"}],"_id":"7512","status":"public","type":"journal_article","article_type":"original","publication":"Journal of Functional Analysis","day":"01","year":"2020","isi":1,"date_created":"2020-02-23T23:00:36Z","date_published":"2020-07-01T00:00:00Z","doi":"10.1016/j.jfa.2020.108507","acknowledgement":"The authors are grateful to Oskari Ajanki for his invaluable help at the initial stage of this project, to Serban Belinschi for useful discussions, to Alexander Tikhomirov for calling our attention to the model example in Section 6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös: Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n","oa":1,"publisher":"Elsevier","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507.","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” Journal of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier, 2020.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 2020;278(12). doi:10.1016/j.jfa.2020.108507","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507"},"title":"Local laws for polynomials of Wigner matrices","external_id":{"arxiv":["1804.11340"],"isi":["000522798900001"]},"article_processing_charge":"No","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","last_name":"Nemish","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X"}],"article_number":"108507","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}]},{"project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"author":[{"first_name":"Jozsef","last_name":"Pitrik","full_name":"Pitrik, Jozsef"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek"}],"article_processing_charge":"No","external_id":{"arxiv":["1903.10455"],"isi":["000551556000002"]},"title":"Quantum Hellinger distances revisited","citation":{"chicago":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” Letters in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s11005-020-01282-0.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","mla":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” Letters in Mathematical Physics, vol. 110, no. 8, Springer Nature, 2020, pp. 2039–52, doi:10.1007/s11005-020-01282-0.","apa":"Pitrik, J., & Virosztek, D. (2020). Quantum Hellinger distances revisited. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01282-0","ama":"Pitrik J, Virosztek D. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 2020;110(8):2039-2052. doi:10.1007/s11005-020-01282-0","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters in Mathematical Physics, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442, K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch, Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21], for comments on earlier versions of this paper, and for several discussions on the topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László Erdös for his essential suggestions on the\r\nstructure and highlights of this paper, and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her valuable comments and suggestions.","page":"2039-2052","date_published":"2020-08-01T00:00:00Z","doi":"10.1007/s11005-020-01282-0","date_created":"2020-03-25T15:57:48Z","isi":1,"year":"2020","day":"01","publication":"Letters in Mathematical Physics","type":"journal_article","article_type":"original","status":"public","_id":"7618","department":[{"_id":"LaEr"}],"date_updated":"2023-08-18T10:17:26Z","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1903.10455","open_access":"1"}],"month":"08","intvolume":" 110","abstract":[{"text":"This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. ","lang":"eng"}],"oa_version":"Preprint","issue":"8","volume":110,"ec_funded":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","language":[{"iso":"eng"}]},{"title":"On the support of the free additive convolution","article_processing_charge":"No","external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"author":[{"orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique. Springer Nature, 2020. https://doi.org/10.1007/s11854-020-0135-2.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. Journal d’Analyse Mathematique. 2020;142:323-348. doi:10.1007/s11854-020-0135-2","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2020). On the support of the free additive convolution. Journal d’Analyse Mathematique. Springer Nature. https://doi.org/10.1007/s11854-020-0135-2","mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique, vol. 142, Springer Nature, 2020, pp. 323–48, doi:10.1007/s11854-020-0135-2."},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_created":"2021-02-07T23:01:15Z","date_published":"2020-11-01T00:00:00Z","doi":"10.1007/s11854-020-0135-2","page":"323-348","publication":"Journal d'Analyse Mathematique","day":"01","year":"2020","isi":1,"oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195.","department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T11:16:03Z","status":"public","type":"journal_article","article_type":"original","_id":"9104","ec_funded":1,"volume":142,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"intvolume":" 142","month":"11","main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5].","lang":"eng"}]},{"department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:08:42Z","type":"journal_article","article_type":"original","keyword":["Analysis"],"status":"public","_id":"10862","ec_funded":1,"volume":279,"issue":"7","publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1708.01597","open_access":"1"}],"scopus_import":"1","intvolume":" 279","month":"10","abstract":[{"lang":"eng","text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix."}],"oa_version":"Preprint","article_processing_charge":"No","external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"title":"Spectral rigidity for addition of random matrices at the regular edge","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108639","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” Journal of Functional Analysis, vol. 279, no. 7. Elsevier, 2020.","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639, Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"108639","date_created":"2022-03-18T10:18:59Z","date_published":"2020-10-15T00:00:00Z","doi":"10.1016/j.jfa.2020.108639","year":"2020","isi":1,"publication":"Journal of Functional Analysis","day":"15","oa":1,"publisher":"Elsevier","quality_controlled":"1","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804."},{"oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","publication":"Random Matrices: Theory and Application","day":"01","year":"2020","isi":1,"date_created":"2019-05-26T21:59:14Z","date_published":"2020-07-01T00:00:00Z","doi":"10.1142/S2010326320500069","article_number":"2050006","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:10.1142/S2010326320500069.","apa":"Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:10.1142/S2010326320500069","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006."},"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","article_processing_charge":"No","external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish."}],"intvolume":" 9","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["20103271"],"issn":["20103263"]},"ec_funded":1,"issue":"3","volume":9,"_id":"6488","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-08-28T08:38:48Z","department":[{"_id":"LaEr"}]},{"isi":1,"has_accepted_license":"1","year":"2020","day":"01","publication":"Communications in Mathematical Physics","page":"1203-1278","doi":"10.1007/s00220-019-03657-4","date_published":"2020-09-01T00:00:00Z","date_created":"2019-03-28T10:21:15Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"citation":{"mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 2020;378:1203-1278. doi:10.1007/s00220-019-03657-4","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"article_processing_charge":"Yes (via OA deal)","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"publication_status":"published","file":[{"creator":"dernst","date_updated":"2020-11-18T11:14:37Z","file_size":2904574,"date_created":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"8771","checksum":"c3a683e2afdcea27afa6880b01e53dc2","success":1}],"language":[{"iso":"eng"}],"volume":378,"related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"ec_funded":1,"abstract":[{"text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"09","intvolume":" 378","date_updated":"2023-09-07T12:54:12Z","ddc":["530","510"],"file_date_updated":"2020-11-18T11:14:37Z","department":[{"_id":"LaEr"}],"_id":"6185","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public"},{"oa":1,"publisher":"EMS Press","quality_controlled":"1","year":"2020","has_accepted_license":"1","publication":"Documenta Mathematica","day":"01","page":"1421-1539","date_created":"2023-12-18T10:37:43Z","date_published":"2020-09-01T00:00:00Z","doi":"10.4171/dm/780","citation":{"ista":"Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica. EMS Press, 2020. https://doi.org/10.4171/dm/780.","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/780","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press, pp. 1421–1539, 2020.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020, pp. 1421–539, doi:10.4171/dm/780."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes","external_id":{"arxiv":["1804.07752"]},"author":[{"last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","abstract":[{"text":"We study the unique solution m of the Dyson equation \\( -m(z)^{-1} = z\\1 - a + S[m(z)] \\) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases.","lang":"eng"}],"oa_version":"Published Version","intvolume":" 25","month":"09","publication_status":"published","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","file_id":"14695","file_size":1374708,"date_updated":"2023-12-18T10:42:32Z","creator":"dernst","file_name":"2020_DocumentaMathematica_Alt.pdf","date_created":"2023-12-18T10:42:32Z"}],"related_material":{"record":[{"relation":"earlier_version","id":"6183","status":"public"}]},"volume":25,"_id":"14694","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","keyword":["General Mathematics"],"status":"public","date_updated":"2023-12-18T10:46:09Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2023-12-18T10:42:32Z"},{"author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"article_processing_charge":"No","external_id":{"isi":["000528269100013"],"arxiv":["1804.07744"]},"title":"Correlated random matrices: Band rigidity and edge universality","citation":{"apa":"Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.","ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"page":"963-1001","date_published":"2020-03-01T00:00:00Z","doi":"10.1214/19-AOP1379","date_created":"2019-03-28T09:20:08Z","isi":1,"year":"2020","day":"01","publication":"Annals of Probability","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"department":[{"_id":"LaEr"}],"date_updated":"2024-02-22T14:34:33Z","type":"journal_article","article_type":"original","status":"public","_id":"6184","related_material":{"record":[{"relation":"dissertation_contains","id":"149","status":"public"},{"id":"6179","status":"public","relation":"dissertation_contains"}]},"issue":"2","volume":48,"ec_funded":1,"publication_identifier":{"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1804.07744","open_access":"1"}],"month":"03","intvolume":" 48","abstract":[{"lang":"eng","text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models."}],"oa_version":"Preprint"},{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” Probability and Mathematical Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2020.1.101","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 2020;1(1):101-146. doi:10.2140/pmp.2020.1.101","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:10.2140/pmp.2020.1.101.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/pmp.2020.1.101."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"external_id":{"arxiv":["1908.01653"]},"article_processing_charge":"No","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","publisher":"Mathematical Sciences Publishers","quality_controlled":"1","oa":1,"year":"2020","day":"16","publication":"Probability and Mathematical Physics","page":"101-146","doi":"10.2140/pmp.2020.1.101","date_published":"2020-11-16T00:00:00Z","date_created":"2024-03-04T10:27:57Z","_id":"15063","type":"journal_article","article_type":"original","status":"public","keyword":["General Medicine"],"date_updated":"2024-03-04T10:33:15Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1908.01653","open_access":"1"}],"month":"11","intvolume":" 1","publication_identifier":{"issn":["2690-1005","2690-0998"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":1,"ec_funded":1},{"type":"journal_article","article_type":"original","status":"public","_id":"15079","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Friedrich","last_name":"Götze","full_name":"Götze, Friedrich"},{"last_name":"Guionnet","full_name":"Guionnet, Alice","first_name":"Alice"}],"article_processing_charge":"No","department":[{"_id":"LaEr"}],"title":"Random matrices","citation":{"ista":"Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527.","chicago":"Erdös, László, Friedrich Götze, and Alice Guionnet. “Random Matrices.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/56.","ama":"Erdös L, Götze F, Guionnet A. Random matrices. Oberwolfach Reports. 2020;16(4):3459-3527. doi:10.4171/owr/2019/56","apa":"Erdös, L., Götze, F., & Guionnet, A. (2020). Random matrices. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/56","short":"L. Erdös, F. Götze, A. Guionnet, Oberwolfach Reports 16 (2020) 3459–3527.","ieee":"L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.","mla":"Erdös, László, et al. “Random Matrices.” Oberwolfach Reports, vol. 16, no. 4, European Mathematical Society, 2020, pp. 3459–527, doi:10.4171/owr/2019/56."},"date_updated":"2024-03-12T12:25:18Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"European Mathematical Society","month":"11","intvolume":" 16","abstract":[{"lang":"eng","text":"Large complex systems tend to develop universal patterns that often represent their essential characteristics. For example, the cumulative effects of independent or weakly dependent random variables often yield the Gaussian universality class via the central limit theorem. For non-commutative random variables, e.g. matrices, the Gaussian behavior is often replaced by another universality class, commonly called random matrix statistics. Nearby eigenvalues are strongly correlated, and, remarkably, their correlation structure is universal, depending only on the symmetry type of the matrix. Even more surprisingly, this feature is not restricted to matrices; in fact Eugene Wigner, the pioneer of the field, discovered in the 1950s that distributions of the gaps between energy levels of complicated quantum systems universally follow the same random matrix statistics. This claim has never been rigorously proved for any realistic physical system but experimental data and extensive numerics leave no doubt as to its correctness. Since then random matrices have proved to be extremely useful phenomenological models in a wide range of applications beyond quantum physics that include number theory, statistics, neuroscience, population dynamics, wireless communication and mathematical finance. The ubiquity of random matrices in natural sciences is still a mystery, but recent years have witnessed a breakthrough in the mathematical description of the statistical structure of their spectrum. Random matrices and closely related areas such as log-gases have become an extremely active research area in probability theory.\r\nThis workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to random matrices. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to stochastic analysis, classical probability theory, operator algebra, supersymmetry, orthogonal polynomials, etc."}],"oa_version":"None","page":"3459-3527","date_published":"2020-11-19T00:00:00Z","doi":"10.4171/owr/2019/56","volume":16,"issue":"4","date_created":"2024-03-05T07:54:44Z","publication_identifier":{"issn":["1660-8933"]},"year":"2020","publication_status":"published","day":"19","publication":"Oberwolfach Reports","language":[{"iso":"eng"}]},{"_id":"7035","conference":{"start_date":"2019-01-28","location":"Kyoto, Japan","end_date":"2019-01-30","name":"Research on isometries as preserver problems and related topics"},"type":"conference","status":"public","citation":{"chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In Kyoto RIMS Kôkyûroku, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.","ista":"Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity. Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related topics vol. 2125, 34–41.","mla":"Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” Kyoto RIMS Kôkyûroku, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric rigidity. In Kyoto RIMS Kôkyûroku (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.","ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: Kyoto RIMS Kôkyûroku. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in Kyoto RIMS Kôkyûroku, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41."},"date_updated":"2021-01-12T08:11:33Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"full_name":"Geher, Gyorgy Pal","last_name":"Geher","first_name":"Gyorgy Pal"},{"full_name":"Titkos, Tamas","last_name":"Titkos","first_name":"Tamas"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511"}],"title":"Dirac masses and isometric rigidity","department":[{"_id":"LaEr"}],"abstract":[{"text":"The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is, the role of Dirac masses by describing the isometry group of various metric spaces of probability measures. This article is of survey character, and it does not contain any essentially new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function spaces. Similarity means here that their isometries are driven by some nice transformations of the underlying space. Of course, it depends on the particular choice of the metric how nice these transformations should be. Sometimes, as we will see, being a homeomorphism is enough to generate an isometry. But sometimes we need more: the transformation must preserve the underlying distance as well. Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As Dirac masses can be considered as building bricks of the set of all Borel measures, a natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses? Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html","open_access":"1"}],"oa":1,"quality_controlled":"1","publisher":"Research Institute for Mathematical Sciences, Kyoto University","intvolume":" 2125","month":"01","year":"2019","publication_status":"published","publication":"Kyoto RIMS Kôkyûroku","language":[{"iso":"eng"}],"day":"30","page":"34-41","date_created":"2019-11-18T15:39:53Z","volume":2125,"date_published":"2019-01-30T00:00:00Z"},{"ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1902.08750","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices.","lang":"eng"}],"department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:17:18Z","status":"public","conference":{"end_date":"2019-07-05","location":"Ljubljana, Slovenia","start_date":"2019-07-01","name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics"},"type":"conference","_id":"8175","date_created":"2020-07-26T22:01:04Z","date_published":"2019-07-01T00:00:00Z","publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","day":"01","year":"2019","oa":1,"quality_controlled":"1","publisher":"Formal Power Series and Algebraic Combinatorics","acknowledgement":"D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models of Section 2.\r\n","title":"New edge asymptotics of skew Young diagrams via free boundaries","article_processing_charge":"No","external_id":{"arxiv":["1902.08750"]},"author":[{"first_name":"Dan","full_name":"Betea, Dan","last_name":"Betea"},{"first_name":"Jérémie","full_name":"Bouttier, Jérémie","last_name":"Bouttier"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"},{"first_name":"Mirjana","full_name":"Vuletíc, Mirjana","last_name":"Vuletíc"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics, 2019.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana, Slovenia, 2019.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.","ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics; 2019.","chicago":"Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics, 2019.","ista":"Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics, 34."},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"article_number":"34"},{"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"author":[{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek"}],"publist_id":"7424","article_processing_charge":"No","external_id":{"arxiv":["1712.05324"],"isi":["000470955300005"]},"title":"Jointly convex quantum Jensen divergences","citation":{"chicago":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications. Elsevier, 2019. https://doi.org/10.1016/j.laa.2018.03.002.","ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78.","mla":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications, vol. 576, Elsevier, 2019, pp. 67–78, doi:10.1016/j.laa.2018.03.002.","ama":"Virosztek D. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 2019;576:67-78. doi:10.1016/j.laa.2018.03.002","apa":"Virosztek, D. (2019). Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2018.03.002","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” Linear Algebra and Its Applications, vol. 576. Elsevier, pp. 67–78, 2019."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office – NKFIH (grant no. K124152)","page":"67-78","date_published":"2019-09-01T00:00:00Z","doi":"10.1016/j.laa.2018.03.002","date_created":"2018-12-11T11:46:17Z","isi":1,"year":"2019","day":"01","publication":"Linear Algebra and Its Applications","article_type":"original","type":"journal_article","status":"public","_id":"405","department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:31:47Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1712.05324"}],"month":"09","intvolume":" 576","abstract":[{"text":"We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.","lang":"eng"}],"oa_version":"Preprint","volume":576,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}]},{"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","oa":1,"publisher":"Springer","quality_controlled":"1","year":"2019","has_accepted_license":"1","isi":1,"publication":"Probability Theory and Related Fields","day":"01","page":"293–373","date_created":"2018-12-11T11:46:25Z","doi":"10.1007/s00440-018-0835-z","date_published":"2019-02-01T00:00:00Z","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"citation":{"ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z","ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.","ista":"Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000459396500007"]},"publist_id":"7394","author":[{"first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","full_name":"Ajanki, Oskari H","last_name":"Ajanki"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"title":"Stability of the matrix Dyson equation and random matrices with correlations","abstract":[{"text":"We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 173","month":"02","publication_status":"published","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"5720","checksum":"f9354fa5c71f9edd17132588f0dc7d01","file_size":1201840,"date_updated":"2020-07-14T12:46:26Z","creator":"dernst","file_name":"2018_ProbTheory_Ajanki.pdf","date_created":"2018-12-17T16:12:08Z"}],"ec_funded":1,"issue":"1-2","volume":173,"_id":"429","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","date_updated":"2023-08-24T14:39:00Z","ddc":["510"],"file_date_updated":"2020-07-14T12:46:26Z","department":[{"_id":"LaEr"}]},{"project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"citation":{"chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2019. https://doi.org/10.1017/etds.2017.52.","ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098.","mla":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:10.1017/etds.2017.52.","apa":"Sadel, C., & Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2017.52","ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 2019;39(4):1082-1098. doi:10.1017/etds.2017.52","ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” Ergodic Theory and Dynamical Systems, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019.","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000459725600012"],"arxiv":["1601.06118"]},"author":[{"last_name":"Sadel","full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian"},{"first_name":"Disheng","last_name":"Xu","full_name":"Xu, Disheng"}],"title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","year":"2019","isi":1,"publication":"Ergodic Theory and Dynamical Systems","day":"01","page":"1082-1098","date_created":"2019-03-10T22:59:18Z","date_published":"2019-04-01T00:00:00Z","doi":"10.1017/etds.2017.52","_id":"6086","type":"journal_article","status":"public","date_updated":"2023-08-25T08:03:30Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov exponent is finite and the st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1601.06118"}],"scopus_import":"1","intvolume":" 39","month":"04","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"volume":39,"issue":"4"},{"date_published":"2019-05-01T00:00:00Z","doi":"10.1214/18-AOP1284","date_created":"2019-06-02T21:59:13Z","page":"1270-1334","day":"01","publication":"Annals of Probability","isi":1,"year":"2019","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"title":"Local single ring theorem on optimal scale","author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"article_processing_charge":"No","external_id":{"arxiv":["1612.05920"],"isi":["000466616100003"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1284","ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. Annals of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:10.1214/18-AOP1284.","ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1284."},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"issue":"3","volume":47,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00911798"]},"publication_status":"published","month":"05","intvolume":" 47","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N)."}],"department":[{"_id":"LaEr"}],"date_updated":"2023-08-28T09:32:29Z","status":"public","type":"journal_article","_id":"6511"},{"volume":480,"issue":"2","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["10960813"],"issn":["0022247X"]},"publication_status":"published","month":"12","intvolume":" 480","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1809.01101","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0
Journal of Mathematical Analysis and Applications, vol. 480, no. 2, 123435, Elsevier, 2019, doi:10.1016/j.jmaa.2019.123435.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” Journal of Mathematical Analysis and Applications, vol. 480, no. 2. Elsevier, 2019.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. Elsevier. https://doi.org/10.1016/j.jmaa.2019.123435","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 2019;480(2). doi:10.1016/j.jmaa.2019.123435","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435.","ista":"Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2), 123435."},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"article_number":"123435"},{"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","page":"441-479","date_created":"2020-01-30T10:36:50Z","date_published":"2019-02-01T00:00:00Z","doi":"10.1214/18-aihp888","year":"2019","isi":1,"publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","day":"01","article_processing_charge":"No","external_id":{"arxiv":["1704.05224"],"isi":["000456070200013"]},"author":[{"last_name":"Akemann","full_name":"Akemann, Gernot","first_name":"Gernot"},{"last_name":"Checinski","full_name":"Checinski, Tomasz","first_name":"Tomasz"},{"first_name":"Dangzheng","id":"2F947E34-F248-11E8-B48F-1D18A9856A87","last_name":"Liu","full_name":"Liu, Dangzheng"},{"last_name":"Strahov","full_name":"Strahov, Eugene","first_name":"Eugene"}],"title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","citation":{"chicago":"Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888.","ista":"Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479.","mla":"Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.","ama":"Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479. doi:10.1214/18-aihp888","apa":"Akemann, G., Checinski, T., Liu, D., & Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888","ieee":"G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles,” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.05224"}],"intvolume":" 55","month":"02","abstract":[{"text":"We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors.","lang":"eng"}],"oa_version":"Preprint","issue":"1","volume":55,"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","_id":"7423","department":[{"_id":"LaEr"}],"date_updated":"2023-09-06T14:58:39Z"},{"_id":"6182","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-09-07T12:54:12Z","file_date_updated":"2020-07-14T12:47:22Z","department":[{"_id":"LaEr"}],"oa_version":"Published Version","abstract":[{"text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion.","lang":"eng"}],"month":"03","intvolume":" 7","scopus_import":"1","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"6883","checksum":"933a472568221c73b2c3ce8c87bf6d15","creator":"dernst","date_updated":"2020-07-14T12:47:22Z","file_size":1520344,"date_created":"2019-09-17T14:24:13Z","file_name":"2019_Forum_Erdoes.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["20505094"]},"publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"volume":7,"ec_funded":1,"article_number":"e8","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2."},"title":"Random matrices with slow correlation decay","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"article_processing_charge":"No","external_id":{"isi":["000488847100001"],"arxiv":["1705.10661"]},"publisher":"Cambridge University Press","quality_controlled":"1","oa":1,"day":"26","publication":"Forum of Mathematics, Sigma","isi":1,"has_accepted_license":"1","year":"2019","date_published":"2019-03-26T00:00:00Z","doi":"10.1017/fms.2019.2","date_created":"2019-03-28T09:05:23Z"},{"page":"615–707","doi":"10.2140/paa.2019.1.615","date_published":"2019-10-12T00:00:00Z","date_created":"2019-03-28T10:21:17Z","year":"2019","day":"12","publication":"Pure and Applied Analysis ","publisher":"MSP","quality_controlled":"1","oa":1,"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"external_id":{"arxiv":["1811.04055"]},"article_processing_charge":"No","title":"Cusp universality for random matrices, II: The real symmetric case","citation":{"ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"issue":"4","volume":1,"related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"ec_funded":1,"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"month":"10","intvolume":" 1","abstract":[{"lang":"eng","text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion."}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","type":"journal_article","article_type":"original","status":"public","_id":"6186"},{"date_updated":"2023-09-08T11:35:31Z","department":[{"_id":"LaEr"}],"_id":"10879","type":"journal_article","article_type":"original","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"status":"public","publication_status":"published","publication_identifier":{"issn":["1664-039X"]},"language":[{"iso":"eng"}],"volume":9,"issue":"3","abstract":[{"lang":"eng","text":"We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H."}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1701.02956","open_access":"1"}],"scopus_import":"1","intvolume":" 9","month":"03","citation":{"apa":"Dietlein, A. M., Gebert, M., & Müller, P. (2019). Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. European Mathematical Society Publishing House. https://doi.org/10.4171/jst/267","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267","ieee":"A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function,” Journal of Spectral Theory, vol. 9, no. 3. European Mathematical Society Publishing House, pp. 921–965, 2019.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267.","ista":"Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 9(3), 921–965.","chicago":"Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory. European Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"author":[{"first_name":"Adrian M","id":"317CB464-F248-11E8-B48F-1D18A9856A87","full_name":"Dietlein, Adrian M","last_name":"Dietlein"},{"last_name":"Gebert","full_name":"Gebert, Martin","first_name":"Martin"},{"last_name":"Müller","full_name":"Müller, Peter","first_name":"Peter"}],"title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","year":"2019","isi":1,"publication":"Journal of Spectral Theory","day":"01","page":"921-965","date_created":"2022-03-18T12:36:42Z","date_published":"2019-03-01T00:00:00Z","doi":"10.4171/jst/267","acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","oa":1,"quality_controlled":"1","publisher":"European Mathematical Society Publishing House"},{"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"month":"09","intvolume":" 55","abstract":[{"text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ<λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t.","lang":"eng"}],"oa_version":"Preprint","issue":"3","volume":55,"ec_funded":1,"publication_identifier":{"issn":["0246-0203"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"72","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"date_updated":"2023-10-17T08:53:45Z","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"page":"1203-1225","date_published":"2019-09-25T00:00:00Z","doi":"10.1214/18-AIHP916","date_created":"2018-12-11T11:44:29Z","isi":1,"year":"2019","day":"25","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"author":[{"first_name":"Patrick","full_name":"Ferrari, Patrick","last_name":"Ferrari"},{"full_name":"Ghosal, Promit","last_name":"Ghosal","first_name":"Promit"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"article_processing_charge":"No","title":"Limit law of a second class particle in TASEP with non-random initial condition","citation":{"ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AIHP916.","apa":"Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AIHP916","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:10.1214/18-AIHP916."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"publisher":"Institut Henri Poincaré","quality_controlled":"1","oa":1,"page":"661-696","doi":"10.1214/18-AIHP894","date_published":"2019-05-01T00:00:00Z","date_created":"2019-04-08T14:05:04Z","isi":1,"year":"2019","day":"01","publication":"Annales de l'institut Henri Poincare","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","last_name":"Nemish","first_name":"Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["1706.08343"],"isi":["000467793600003"]},"title":"Location of the spectrum of Kronecker random matrices","citation":{"mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:10.1214/18-AIHP894.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894","ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696. doi:10.1214/18-AIHP894","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.","ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1706.08343","open_access":"1"}],"month":"05","intvolume":" 55","abstract":[{"lang":"eng","text":"For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles."}],"oa_version":"Preprint","issue":"2","related_material":{"record":[{"relation":"dissertation_contains","id":"149","status":"public"}]},"volume":55,"ec_funded":1,"publication_identifier":{"issn":["0246-0203"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"6240","department":[{"_id":"LaEr"}],"date_updated":"2023-10-17T12:20:20Z"},{"author":[{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"article_processing_charge":"No","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","citation":{"mla":"Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:10.15479/AT:ISTA:th6179","apa":"Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179","chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"page":"375","date_published":"2019-03-18T00:00:00Z","doi":"10.15479/AT:ISTA:th6179","date_created":"2019-03-28T08:58:59Z","has_accepted_license":"1","year":"2019","day":"18","publisher":"Institute of Science and Technology Austria","oa":1,"file_date_updated":"2020-07-14T12:47:21Z","department":[{"_id":"LaEr"}],"supervisor":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"}],"date_updated":"2024-02-22T14:34:33Z","ddc":["515","519"],"type":"dissertation","status":"public","_id":"6179","related_material":{"record":[{"status":"public","id":"1144","relation":"part_of_dissertation"},{"status":"public","id":"6186","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"6185"},{"relation":"part_of_dissertation","id":"6182","status":"public"},{"relation":"part_of_dissertation","id":"1012","status":"public"},{"relation":"part_of_dissertation","id":"6184","status":"public"}]},"ec_funded":1,"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"checksum":"6926f66f28079a81c4937e3764be00fc","file_id":"6180","relation":"source_file","access_level":"closed","content_type":"application/x-gzip","file_name":"2019_Schroeder_Thesis.tar.gz","date_created":"2019-03-28T08:53:52Z","creator":"dernst","file_size":7104482,"date_updated":"2020-07-14T12:47:21Z"},{"date_created":"2019-03-28T08:53:52Z","file_name":"2019_Schroeder_Thesis.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:21Z","file_size":4228794,"checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","file_id":"6181","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"month":"03","abstract":[{"text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure.","lang":"eng"}],"oa_version":"Published Version"},{"oa":1,"quality_controlled":"1","publisher":"Springer","date_created":"2018-12-11T11:47:56Z","doi":"10.1007/s00440-017-0787-8","date_published":"2018-06-14T00:00:00Z","year":"2018","publication":"Probability Theory and Related Fields","day":"14","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"543-616","external_id":{"arxiv":["1605.08767"]},"author":[{"last_name":"Lee","full_name":"Lee, Jii","first_name":"Jii"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli"}],"publist_id":"7017","title":"Local law and Tracy–Widom limit for sparse random matrices","citation":{"chicago":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields. Springer, 2018. https://doi.org/10.1007/s00440-017-0787-8.","ista":"Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 171(1–2), 543–616.","mla":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616, Springer, 2018, doi:10.1007/s00440-017-0787-8.","ama":"Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8","apa":"Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8","ieee":"J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random matrices,” Probability Theory and Related Fields, vol. 171, no. 1–2. Springer, 2018.","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1605.08767","open_access":"1"}],"scopus_import":1,"intvolume":" 171","month":"06","abstract":[{"text":"We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":171,"issue":"1-2","publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"690","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:09:33Z"},{"page":"148-203","doi":"10.1214/17-AAP1302","date_published":"2018-03-03T00:00:00Z","date_created":"2018-12-11T11:47:13Z","isi":1,"year":"2018","day":"03","publication":"Annals Applied Probability ","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297"}],"article_processing_charge":"No","external_id":{"isi":["000431721800005"],"arxiv":["1612.07776 "]},"title":"Local inhomogeneous circular law","citation":{"ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability . Institute of Mathematical Statistics. https://doi.org/10.1214/17-AAP1302","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.","mla":"Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018, pp. 148–203, doi:10.1214/17-AAP1302.","ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/17-AAP1302."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"issue":"1","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"}]},"volume":28,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.07776 "}],"month":"03","intvolume":" 28","abstract":[{"text":"We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. [11,12] shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. \r\n\r\n","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-09-13T08:47:52Z","article_type":"original","type":"journal_article","status":"public","_id":"566"},{"_id":"181","type":"journal_article","status":"public","date_updated":"2023-09-15T12:05:52Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1708.01546","open_access":"1"}],"month":"01","intvolume":" 50","publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":50,"ec_funded":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"name":"Structured Non-Hermitian Random Matrices","grant_number":"M02080","call_identifier":"FWF","_id":"258F40A4-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.","ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125","apa":"Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","full_name":"Renfrew, David T","orcid":"0000-0003-3493-121X","last_name":"Renfrew"}],"publist_id":"7740","article_processing_charge":"No","external_id":{"arxiv":["1708.01546"],"isi":["000437018500032"]},"title":"Power law decay for systems of randomly coupled differential equations","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1,"isi":1,"year":"2018","day":"01","publication":"SIAM Journal on Mathematical Analysis","page":"3271 - 3290","doi":"10.1137/17M1143125","date_published":"2018-01-01T00:00:00Z","date_created":"2018-12-11T11:45:03Z"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096","apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096.","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096."},"title":"Bounds on the norm of Wigner-type random matrices","article_processing_charge":"No","external_id":{"isi":["000477677200002"],"arxiv":["1802.05175"]},"author":[{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mühlbacher","full_name":"Mühlbacher, Peter","first_name":"Peter"}],"article_number":"1950009","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"publication":"Random matrices: Theory and applications","day":"26","year":"2018","isi":1,"date_created":"2019-02-13T10:40:54Z","doi":"10.1142/s2010326319500096","date_published":"2018-09-26T00:00:00Z","oa":1,"publisher":"World Scientific Publishing","quality_controlled":"1","date_updated":"2023-09-19T14:24:05Z","department":[{"_id":"LaEr"}],"_id":"5971","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"ec_funded":1,"oa_version":"Preprint","abstract":[{"text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation.","lang":"eng"}],"month":"09","main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"scopus_import":"1"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330","apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.","ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330."},"title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","article_processing_charge":"No","external_id":{"arxiv":["1608.05163"],"isi":["000441668300009"]},"publist_id":"6383","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publication":"International Mathematics Research Notices","day":"18","year":"2018","isi":1,"date_created":"2018-12-11T11:49:41Z","date_published":"2018-05-18T00:00:00Z","doi":"10.1093/imrn/rnw330","page":"3255-3298","oa":1,"quality_controlled":"1","publisher":"Oxford University Press","date_updated":"2023-09-22T09:44:21Z","department":[{"_id":"LaEr"}],"_id":"1012","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["10737928"]},"ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"issue":"10","volume":2018,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense."}],"intvolume":" 2018","month":"05","main_file_link":[{"url":"https://arxiv.org/abs/1608.05163","open_access":"1"}],"scopus_import":"1"},{"ddc":["510"],"date_updated":"2023-10-10T13:11:29Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:46Z","_id":"70","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"5981","checksum":"2ded46aa284a836a8cbb34133a64f1cb","date_updated":"2020-07-14T12:47:46Z","file_size":394851,"creator":"kschuh","date_created":"2019-02-14T09:44:10Z","file_name":"2018_ALEA_Nejjar.pdf"}],"publication_status":"published","publication_identifier":{"issn":["1980-0436"]},"ec_funded":1,"issue":"2","volume":15,"oa_version":"Published Version","abstract":[{"text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.","lang":"eng"}],"intvolume":" 15","month":"10","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49."},"title":"Transition to shocks in TASEP and decoupling of last passage times","article_processing_charge":"No","external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"author":[{"last_name":"Nejjar","full_name":"Nejjar, Peter","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"publication":"Latin American Journal of Probability and Mathematical Statistics","day":"01","year":"2018","has_accepted_license":"1","isi":1,"date_created":"2018-12-11T11:44:28Z","doi":"10.30757/ALEA.v15-49","date_published":"2018-10-01T00:00:00Z","page":"1311-1334","oa":1,"quality_controlled":"1","publisher":"Instituto Nacional de Matematica Pura e Aplicada"},{"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"author":[{"full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7615","external_id":{"arxiv":["1802.03305"]},"article_processing_charge":"No","title":"Maps on probability measures preserving certain distances - a survey and some new results","citation":{"ista":"Virosztek D. 2018. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80.","chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.","short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. Springer Nature. https://doi.org/10.14232/actasm-018-753-y","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).","page":"65 - 80","doi":"10.14232/actasm-018-753-y","date_published":"2018-06-04T00:00:00Z","date_created":"2018-12-11T11:45:36Z","year":"2018","day":"04","publication":"Acta Scientiarum Mathematicarum","type":"journal_article","article_type":"original","status":"public","_id":"284","department":[{"_id":"LaEr"}],"date_updated":"2023-10-16T10:29:22Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.03305"}],"month":"06","intvolume":" 84","abstract":[{"text":"Borel probability measures living on metric spaces are fundamental\r\nmathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere.","lang":"eng"}],"oa_version":"Preprint","issue":"1-2","volume":84,"ec_funded":1,"publication_identifier":{"issn":["0001-6969"],"eissn":["2064-8316"]},"publication_status":"published","language":[{"iso":"eng"}]},{"article_number":"1804.07752","_id":"6183","status":"public","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, 1804.07752.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” arXiv. .","short":"J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.).","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d.","ista":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv, 1804.07752."},"date_updated":"2023-12-18T10:46:08Z","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","department":[{"_id":"LaEr"}],"external_id":{"arxiv":["1804.07752"]},"article_processing_charge":"No","author":[{"last_name":"Alt","full_name":"Alt, Johannes","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure, which\r\nis supported on finitely many intervals, called bands. In fact, the density is\r\nanalytic inside the bands with a square-root growth at the edges and internal\r\ncubic root cusps whenever the gap between two bands vanishes. The shape of\r\nthese singularities is universal and no other singularity may occur. We give a\r\nprecise asymptotic description of $m$ near the singular points. These\r\nasymptotics generalize the analysis at the regular edges given in the companion\r\npaper on the Tracy-Widom universality for the edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744] and they play a key role in the\r\nproof of the Pearcey universality at the cusp for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically rigid under\r\ndeformations and we conclude that these masses are quantized in some important\r\ncases."}],"month":"04","main_file_link":[{"url":"https://arxiv.org/abs/1804.07752","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"publication":"arXiv","day":"20","publication_status":"submitted","year":"2018","date_created":"2019-03-28T09:20:06Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"},{"relation":"later_version","status":"public","id":"14694"}]},"date_published":"2018-04-20T00:00:00Z"},{"abstract":[{"text":"We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"11","intvolume":" 19","publication_identifier":{"issn":["1424-0637"]},"publication_status":"published","file":[{"file_id":"5866","checksum":"0c38abe73569b7166b7487ad5d23cc68","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2018_Annales_Betea.pdf","date_created":"2019-01-21T15:18:55Z","file_size":3084674,"date_updated":"2020-07-14T12:47:03Z","creator":"dernst"}],"language":[{"iso":"eng"}],"volume":19,"issue":"12","ec_funded":1,"_id":"556","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2024-02-20T10:48:17Z","ddc":["500"],"file_date_updated":"2020-07-14T12:47:03Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"quality_controlled":"1","publisher":"Springer Nature","oa":1,"has_accepted_license":"1","year":"2018","day":"13","publication":"Annales Henri Poincare","page":"3663-3742","date_published":"2018-11-13T00:00:00Z","doi":"10.1007/s00023-018-0723-1","date_created":"2018-12-11T11:47:09Z","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"citation":{"ama":"Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-018-0723-1","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018.","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.","ista":"Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742.","chicago":"Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Betea","full_name":"Betea, Dan","first_name":"Dan"},{"first_name":"Jeremie","full_name":"Bouttier, Jeremie","last_name":"Bouttier"},{"last_name":"Nejjar","full_name":"Nejjar, Peter","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vuletic, Mirjana","last_name":"Vuletic","first_name":"Mirjana"}],"publist_id":"7258","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1704.05809"]},"title":"The free boundary Schur process and applications I"},{"_id":"149","pubrep_id":"1040","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","ddc":["515","519"],"date_updated":"2024-02-22T14:34:33Z","supervisor":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"}],"file_date_updated":"2020-07-14T12:44:57Z","department":[{"_id":"LaEr"}],"oa_version":"Published Version","abstract":[{"text":"The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations.","lang":"eng"}],"month":"07","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"file":[{"file_size":5801709,"date_updated":"2020-07-14T12:44:57Z","creator":"dernst","file_name":"2018_thesis_Alt.pdf","date_created":"2019-04-08T13:55:20Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"6241","checksum":"d4dad55a7513f345706aaaba90cb1bb8"},{"creator":"dernst","date_updated":"2020-07-14T12:44:57Z","file_size":3802059,"date_created":"2019-04-08T13:55:20Z","file_name":"2018_thesis_Alt_source.zip","access_level":"closed","relation":"source_file","content_type":"application/zip","checksum":"d73fcf46300dce74c403f2b491148ab4","file_id":"6242"}],"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1677"},{"status":"public","id":"550","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"6183"},{"status":"public","id":"566","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"1010"},{"status":"public","id":"6240","relation":"part_of_dissertation"},{"status":"public","id":"6184","relation":"part_of_dissertation"}]},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria.","chicago":"Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040.","ama":"Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040","apa":"Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040","ieee":"J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute of Science and Technology Austria, 2018.","short":"J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.","mla":"Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040."},"title":"Dyson equation and eigenvalue statistics of random matrices","article_processing_charge":"No","author":[{"full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"}],"publist_id":"7772","oa":1,"publisher":"Institute of Science and Technology Austria","day":"12","year":"2018","has_accepted_license":"1","date_created":"2018-12-11T11:44:53Z","doi":"10.15479/AT:ISTA:TH_1040","date_published":"2018-07-12T00:00:00Z","page":"456"},{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"title":"Universality for a class of random band matrices","publist_id":"7337","author":[{"first_name":"Paul","last_name":"Bourgade","full_name":"Bourgade, Paul"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng"},{"first_name":"Jun","full_name":"Yin, Jun","last_name":"Yin"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800. doi:10.4310/ATMP.2017.v21.n3.a5","apa":"Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.","mla":"Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.","ista":"Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.","chicago":"Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5."},"oa":1,"publisher":"International Press","quality_controlled":"1","date_created":"2018-12-11T11:46:43Z","date_published":"2017-08-25T00:00:00Z","doi":"10.4310/ATMP.2017.v21.n3.a5","page":"739 - 800","publication":"Advances in Theoretical and Mathematical Physics","day":"25","year":"2017","status":"public","type":"journal_article","_id":"483","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:00:57Z","intvolume":" 21","month":"08","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02312"}],"scopus_import":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices."}],"ec_funded":1,"volume":21,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["10950761"]}},{"alternative_title":["Courant Lecture Notes"],"month":"01","intvolume":" 28","abstract":[{"text":"This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n","lang":"eng"}],"oa_version":"None","volume":28,"ec_funded":1,"publication_identifier":{"isbn":["9-781-4704-3648-3"],"eisbn":["978-1-4704-4194-4"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"book","status":"public","series_title":"Courant Lecture Notes","_id":"567","department":[{"_id":"LaEr"}],"date_updated":"2022-05-24T06:57:28Z","publisher":"American Mathematical Society","quality_controlled":"1","page":"226","date_published":"2017-01-01T00:00:00Z","doi":"10.1090/cln/028","date_created":"2018-12-11T11:47:13Z","year":"2017","day":"01","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"last_name":"Yau","full_name":"Yau, Horng","first_name":"Horng"}],"publist_id":"7247","article_processing_charge":"No","title":"A Dynamical Approach to Random Matrix Theory","citation":{"mla":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.","ieee":"L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory, vol. 28. American Mathematical Society, 2017.","short":"L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017.","ama":"Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28. American Mathematical Society; 2017. doi:10.1090/cln/028","apa":"Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory (Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028","chicago":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017. https://doi.org/10.1090/cln/028.","ista":"Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 226p."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"short":"L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656.","ieee":"L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017.","apa":"Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 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Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AIHP765."},"title":"Universality for random matrix flows with time dependent density","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"publist_id":"7189","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"01","year":"2017","date_created":"2018-12-11T11:47:30Z","date_published":"2017-11-01T00:00:00Z","doi":"10.1214/16-AIHP765","page":"1606 - 1656","_id":"615","status":"public","type":"journal_article","date_updated":"2021-01-12T08:06:22Z","department":[{"_id":"LaEr"}],"oa_version":"Submitted Version","abstract":[{"text":"We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion of the eigenvalues hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from Wigner's semicircle law.","lang":"eng"}],"intvolume":" 53","month":"11","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1504.00650"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["02460203"]},"ec_funded":1,"volume":53,"issue":"4"},{"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur."}],"month":"09","intvolume":" 70","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1512.03703"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00103640"]},"publication_status":"published","volume":70,"issue":"9","ec_funded":1,"_id":"721","status":"public","type":"journal_article","date_updated":"2021-01-12T08:12:24Z","department":[{"_id":"LaEr"}],"publisher":"Wiley-Blackwell","quality_controlled":"1","oa":1,"day":"01","publication":"Communications on Pure and Applied Mathematics","year":"2017","date_published":"2017-09-01T00:00:00Z","doi":"10.1002/cpa.21639","date_created":"2018-12-11T11:48:08Z","page":"1672 - 1705","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics. 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Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.","short":"O.H. Ajanki, T.H. Krüger, L. 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We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities."}],"oa_version":"Published Version","scopus_import":1,"month":"11","intvolume":" 22","date_updated":"2023-09-07T12:38:08Z","ddc":["539"],"file_date_updated":"2020-07-14T12:47:00Z","department":[{"_id":"LaEr"}],"_id":"550","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"926","has_accepted_license":"1","year":"2017","day":"21","publication":"Electronic Communications in Probability","doi":"10.1214/17-ECP97","date_published":"2017-11-21T00:00:00Z","date_created":"2018-12-11T11:47:07Z","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"citation":{"short":"J. 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Electronic Communications in Probability. 22, 63.","chicago":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-ECP97."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"}],"publist_id":"7265","title":"Singularities of the density of states of random Gram matrices","article_number":"63","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}]},{"ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"volume":21,"language":[{"iso":"eng"}],"file":[{"file_name":"IST-2017-747-v1+1_euclid.ecp.1483347665.pdf","date_created":"2018-12-12T10:18:10Z","creator":"system","file_size":440770,"date_updated":"2018-12-12T10:18:10Z","file_id":"5329","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"publication_status":"published","intvolume":" 21","month":"01","scopus_import":1,"oa_version":"Published Version","abstract":[{"text":"We show that matrix elements of functions of N × N Wigner matrices fluctuate on a scale of order N−1/2 and we identify the limiting fluctuation. Our result holds for any function f of the matrix that has bounded variation thus considerably relaxing the regularity requirement imposed in [7, 11].","lang":"eng"}],"file_date_updated":"2018-12-12T10:18:10Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-09-07T12:54:12Z","pubrep_id":"747","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"1144","date_created":"2018-12-11T11:50:23Z","doi":"10.1214/16-ECP38","date_published":"2017-01-02T00:00:00Z","publication":"Electronic Communications in Probability","day":"02","year":"2017","has_accepted_license":"1","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","acknowledgement":"Partially supported by the IST Austria Excellence Scholarship.","title":"Fluctuations of functions of Wigner matrices","publist_id":"6214","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 21, 86.","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-ECP38.","short":"L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.","apa":"Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-ECP38","ama":"Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 2017;21. doi:10.1214/16-ECP38","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability, vol. 21, 86, Institute of Mathematical Statistics, 2017, doi:10.1214/16-ECP38."},"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"article_number":"86"},{"title":"Delocalization for a class of random block band matrices","publist_id":"5644","author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000398842700004"]},"article_processing_charge":"Yes (via OA deal)","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776.","chicago":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-015-0692-y.","short":"Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.","ieee":"Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.","ama":"Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y","apa":"Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y","mla":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4, Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y."},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"doi":"10.1007/s00440-015-0692-y","date_published":"2017-04-01T00:00:00Z","date_created":"2018-12-11T11:52:32Z","page":"673 - 776","day":"01","publication":"Probability Theory and Related Fields","has_accepted_license":"1","isi":1,"year":"2017","publisher":"Springer","quality_controlled":"1","oa":1,"acknowledgement":"Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L. Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to the anonymous referees for careful reading and valuable comments, which helped to improve the organization.","department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:45:00Z","ddc":["530"],"date_updated":"2023-09-20T09:42:12Z","status":"public","pubrep_id":"489","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"1528","volume":167,"issue":"3-4","ec_funded":1,"file":[{"date_created":"2018-12-12T10:08:05Z","file_name":"IST-2016-489-v1+1_s00440-015-0692-y.pdf","date_updated":"2020-07-14T12:45:00Z","file_size":1615755,"creator":"system","file_id":"4665","checksum":"67afa85ff1e220cbc1f9f477a828513c","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["01788051"]},"publication_status":"published","month":"04","intvolume":" 167","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.","lang":"eng"}]},{"file":[{"file_id":"4686","checksum":"29f5a72c3f91e408aeb9e78344973803","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:08:25Z","file_name":"IST-2017-657-v1+2_s00440-016-0740-2.pdf","creator":"system","date_updated":"2020-07-14T12:44:44Z","file_size":988843}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["01788051"]},"publication_status":"published","volume":169,"issue":"3-4","ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=\\mathbbmE|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z)) solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes.","lang":"eng"}],"month":"12","intvolume":" 169","scopus_import":"1","ddc":["510","530"],"date_updated":"2023-09-20T11:14:17Z","file_date_updated":"2020-07-14T12:44:44Z","department":[{"_id":"LaEr"}],"_id":"1337","status":"public","pubrep_id":"657","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","publication":"Probability Theory and Related Fields","isi":1,"has_accepted_license":"1","year":"2017","date_published":"2017-12-01T00:00:00Z","doi":"10.1007/s00440-016-0740-2","date_created":"2018-12-11T11:51:27Z","page":"667 - 727","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","publisher":"Springer","quality_controlled":"1","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields, vol. 169, no. 3–4, Springer, 2017, pp. 667–727, doi:10.1007/s00440-016-0740-2.","ama":"Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 2017;169(3-4):667-727. doi:10.1007/s00440-016-0740-2","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-016-0740-2","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-016-0740-2.","ista":"Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727."},"title":"Universality for general Wigner-type matrices","author":[{"full_name":"Ajanki, Oskari H","last_name":"Ajanki","first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"publist_id":"5930","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000414358400002"]},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}]},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:10.1007/s00220-016-2805-6.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017.","short":"Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2805-6","ama":"Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990."},"title":"Local law of addition of random matrices on optimal scale","external_id":{"isi":["000393696700005"]},"article_processing_charge":"Yes (via OA deal)","publist_id":"6141","author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publication":"Communications in Mathematical Physics","day":"01","year":"2017","has_accepted_license":"1","isi":1,"date_created":"2018-12-11T11:50:43Z","doi":"10.1007/s00220-016-2805-6","date_published":"2017-02-01T00:00:00Z","page":"947 - 990","oa":1,"quality_controlled":"1","publisher":"Springer","ddc":["530"],"date_updated":"2023-09-20T11:16:57Z","department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:44:39Z","_id":"1207","pubrep_id":"722","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:44:39Z","file_size":1033743,"creator":"system","date_created":"2018-12-12T10:14:47Z","file_name":"IST-2016-722-v1+1_s00220-016-2805-6.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"ddff79154c3daf27237de5383b1264a9","file_id":"5102"}],"publication_status":"published","publication_identifier":{"issn":["00103616"]},"ec_funded":1,"volume":349,"issue":"3","oa_version":"Published Version","abstract":[{"text":"The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.","lang":"eng"}],"intvolume":" 349","month":"02","scopus_import":"1"},{"department":[{"_id":"LaEr"}],"file_date_updated":"2018-12-12T10:15:29Z","ddc":["510"],"date_updated":"2023-09-22T09:27:51Z","pubrep_id":"802","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"1023","volume":22,"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"5149","creator":"system","date_updated":"2018-12-12T10:15:29Z","file_size":742275,"date_created":"2018-12-12T10:15:29Z","file_name":"IST-2017-802-v1+1_euclid.ejp.1487991681.pdf"}],"publication_status":"published","publication_identifier":{"issn":["10836489"]},"intvolume":" 22","month":"02","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We consider products of independent square non-Hermitian random matrices. More precisely, let X1,…, Xn be independent N × N random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance 1/N. Soshnikov-O’Rourke [19] and Götze-Tikhomirov [15] showed that the empirical spectral distribution of the product of n random matrices with iid entries converges to (equation found). We prove that if the entries of the matrices X1,…, Xn are independent (but not necessarily identically distributed) and satisfy uniform subexponential decay condition, then in the bulk the convergence of the ESD of X1,…, Xn to (0.1) holds up to the scale N–1/2+ε.","lang":"eng"}],"title":"Local law for the product of independent non-Hermitian random matrices with independent entries","article_processing_charge":"No","external_id":{"isi":["000396611900022"]},"publist_id":"6370","author":[{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","last_name":"Nemish"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP38.","ista":"Nemish Y. 2017. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 22, 22.","mla":"Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” Electronic Journal of Probability, vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP38.","short":"Y. Nemish, Electronic Journal of Probability 22 (2017).","ieee":"Y. Nemish, “Local law for the product of independent non-Hermitian random matrices with independent entries,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.","ama":"Nemish Y. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP38","apa":"Nemish, Y. (2017). Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP38"},"article_number":"22","date_created":"2018-12-11T11:49:44Z","date_published":"2017-02-06T00:00:00Z","doi":"10.1214/17-EJP38","publication":"Electronic Journal of Probability","day":"06","year":"2017","has_accepted_license":"1","isi":1,"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1"},{"oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","date_created":"2018-12-11T11:49:40Z","doi":"10.1214/17-EJP42","date_published":"2017-03-08T00:00:00Z","publication":"Electronic Journal of Probability","day":"08","year":"2017","isi":1,"has_accepted_license":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"25","title":"Local law for random Gram matrices","external_id":{"arxiv":["1606.07353"],"isi":["000396611900025"]},"article_processing_charge":"No","publist_id":"6386","author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","last_name":"Alt"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42.","ama":"Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP42","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP42","short":"J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP42.","ista":"Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25."},"intvolume":" 22","month":"03","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances. The limiting eigenvalue density that generalizes the Marchenko-Pastur law is determined by solving a system of nonlinear equations. Our entrywise and averaged local laws are on the optimal scale with the optimal error bounds. They hold both in the square case (hard edge) and in the properly rectangular case (soft edge). In the latter case we also establish a macroscopic gap away from zero in the spectrum of XX∗. ","lang":"eng"}],"ec_funded":1,"volume":22,"related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-12T10:13:39Z","file_name":"IST-2017-807-v1+1_euclid.ejp.1488942016.pdf","creator":"system","date_updated":"2018-12-12T10:13:39Z","file_size":639384,"file_id":"5024","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["10836489"]},"pubrep_id":"807","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"1010","file_date_updated":"2018-12-12T10:13:39Z","department":[{"_id":"LaEr"}],"ddc":["510","539"],"date_updated":"2023-09-22T09:45:23Z"},{"department":[{"_id":"LaEr"}],"date_updated":"2023-09-28T11:30:42Z","status":"public","type":"journal_article","_id":"733","ec_funded":1,"volume":319,"language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 319","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1606.03076","open_access":"1"}],"scopus_import":"1","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum."}],"title":"Convergence rate for spectral distribution of addition of random matrices","external_id":{"isi":["000412150400010"]},"article_processing_charge":"No","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"}],"publist_id":"6935","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.","mla":"Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics, vol. 319, Academic Press, 2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028.","ama":"Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2017.08.028","short":"Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017."},"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"date_created":"2018-12-11T11:48:13Z","doi":"10.1016/j.aim.2017.08.028","date_published":"2017-10-15T00:00:00Z","page":"251 - 291","publication":"Advances in Mathematics","day":"15","year":"2017","isi":1,"oa":1,"quality_controlled":"1","publisher":"Academic Press","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation"},{"department":[{"_id":"LaEr"},{"_id":"JaMa"}],"date_updated":"2023-10-10T13:10:32Z","article_type":"original","type":"journal_article","status":"public","_id":"447","volume":9,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"http://alea.impa.br/articles/v14/14-17.pdf"}],"month":"03","intvolume":" 9","abstract":[{"text":"We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).","lang":"eng"}],"oa_version":"Submitted Version","author":[{"first_name":"Patrik","full_name":"Ferrari, Patrik","last_name":"Ferrari"},{"last_name":"Nejjar","full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"}],"publist_id":"7376","article_processing_charge":"No","title":"Fluctuations of the competition interface in presence of shocks","citation":{"ieee":"P. Ferrari and P. Nejjar, “Fluctuations of the competition interface in presence of shocks,” Revista Latino-Americana de Probabilidade e Estatística, vol. 9. Instituto Nacional de Matematica Pura e Aplicada, pp. 299–325, 2017.","short":"P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 299–325.","ama":"Ferrari P, Nejjar P. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 2017;9:299-325. doi:10.30757/ALEA.v14-17","apa":"Ferrari, P., & Nejjar, P. (2017). Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v14-17","mla":"Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística, vol. 9, Instituto Nacional de Matematica Pura e Aplicada, 2017, pp. 299–325, doi:10.30757/ALEA.v14-17.","ista":"Ferrari P, Nejjar P. 2017. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 9, 299–325.","chicago":"Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada, 2017. https://doi.org/10.30757/ALEA.v14-17."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"page":"299 - 325","date_published":"2017-03-23T00:00:00Z","doi":"10.30757/ALEA.v14-17","date_created":"2018-12-11T11:46:31Z","year":"2017","day":"23","publication":"Revista Latino-Americana de Probabilidade e Estatística","publisher":"Instituto Nacional de Matematica Pura e Aplicada","quality_controlled":"1","oa":1},{"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"volume":26,"issue":"6","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where the sample X is an M ×N random matrix whose entries are real independent random variables with variance 1/N and whereσ is an M × M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class of populations σ in the sub-critical regime, we show that the distribution of the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians or (2) that σ is diagonal and that the entries of X have a sub-exponential decay."}],"intvolume":" 26","month":"12","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1409.4979"}],"scopus_import":1,"date_updated":"2021-01-12T06:48:43Z","department":[{"_id":"LaEr"}],"_id":"1157","status":"public","type":"journal_article","publication":"Annals of Applied Probability","day":"15","year":"2016","date_created":"2018-12-11T11:50:27Z","doi":"10.1214/16-AAP1193","date_published":"2016-12-15T00:00:00Z","page":"3786 - 3839","acknowledgement":"We thank Horng-Tzer Yau for numerous discussions and remarks. We are grateful to Ben Adlam, Jinho Baik, Zhigang Bao, Paul Bourgade, László Erd ̋os, Iain Johnstone and Antti Knowles for comments. We are also grate-\r\nful to the anonymous referee for carefully reading our manuscript and suggesting several improvements.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Lee J, Schnelli K. 2016. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. 26(6), 3786–3839.","chicago":"Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals of Applied Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/16-AAP1193.","ieee":"J. Lee and K. Schnelli, “Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population,” Annals of Applied Probability, vol. 26, no. 6. Institute of Mathematical Statistics, pp. 3786–3839, 2016.","short":"J. Lee, K. Schnelli, Annals of Applied Probability 26 (2016) 3786–3839.","apa":"Lee, J., & Schnelli, K. (2016). Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AAP1193","ama":"Lee J, Schnelli K. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. 2016;26(6):3786-3839. doi:10.1214/16-AAP1193","mla":"Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals of Applied Probability, vol. 26, no. 6, Institute of Mathematical Statistics, 2016, pp. 3786–839, doi:10.1214/16-AAP1193."},"title":"Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population","author":[{"first_name":"Ji","last_name":"Lee","full_name":"Lee, Ji"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli"}],"publist_id":"6201","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]},{"ec_funded":1,"volume":44,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 44","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1405.6634","open_access":"1"}],"scopus_import":1,"oa_version":"Preprint","abstract":[{"text":"We consider N×N random matrices of the form H = W + V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues ofW and V are typically of the same order. For a large class of diagonal matrices V , we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.","lang":"eng"}],"department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:49:10Z","status":"public","type":"journal_article","_id":"1219","date_created":"2018-12-11T11:50:47Z","date_published":"2016-01-01T00:00:00Z","doi":"10.1214/15-AOP1023","page":"2349 - 2425","publication":"Annals of Probability","day":"01","year":"2016","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","acknowledgement":"J.C. was supported in part by National Research Foundation of Korea Grant 2011-0013474 and TJ Park Junior Faculty Fellowship.\r\nK.S. was supported by ERC Advanced Grant RANMAT, No. 338804, and the \"Fund for Math.\"\r\nB.S. was supported by NSF GRFP Fellowship DGE-1144152.\r\nH.Y. was supported in part by NSF Grant DMS-13-07444 and Simons investigator fellowship. We thank Paul Bourgade, László Erd ̋os and Antti Knowles for helpful comments. We are grateful to the Taida Institute for Mathematical\r\nSciences and National Taiwan Universality for their hospitality during part of this\r\nresearch. We thank Thomas Spencer and the Institute for Advanced Study for their\r\nhospitality during the academic year 2013–2014. ","title":"Bulk universality for deformed wigner matrices","author":[{"first_name":"Jioon","full_name":"Lee, Jioon","last_name":"Lee"},{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Stetler","full_name":"Stetler, Ben","first_name":"Ben"},{"first_name":"Horngtzer","last_name":"Yau","full_name":"Yau, Horngtzer"}],"publist_id":"6115","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Lee, Jioon, Kevin Schnelli, Ben Stetler, and Horngtzer Yau. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/15-AOP1023.","ista":"Lee J, Schnelli K, Stetler B, Yau H. 2016. Bulk universality for deformed wigner matrices. Annals of Probability. 44(3), 2349–2425.","mla":"Lee, Jioon, et al. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability, vol. 44, no. 3, Institute of Mathematical Statistics, 2016, pp. 2349–425, doi:10.1214/15-AOP1023.","apa":"Lee, J., Schnelli, K., Stetler, B., & Yau, H. (2016). Bulk universality for deformed wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/15-AOP1023","ama":"Lee J, Schnelli K, Stetler B, Yau H. Bulk universality for deformed wigner matrices. Annals of Probability. 2016;44(3):2349-2425. doi:10.1214/15-AOP1023","short":"J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 2349–2425.","ieee":"J. Lee, K. Schnelli, B. Stetler, and H. Yau, “Bulk universality for deformed wigner matrices,” Annals of Probability, vol. 44, no. 3. Institute of Mathematical Statistics, pp. 2349–2425, 2016."},"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}]},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory. European Mathematical Society, 2016. https://doi.org/10.4171/JST/132.","ista":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. 2016. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 6(3), 557–600.","mla":"Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory, vol. 6, no. 3, European Mathematical Society, 2016, pp. 557–600, doi:10.4171/JST/132.","short":"R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 557–600.","ieee":"R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally periodic random potentials on binary trees,” Journal of Spectral Theory, vol. 6, no. 3. European Mathematical Society, pp. 557–600, 2016.","apa":"Froese, R., Lee, D., Sadel, C., Spitzer, W., & Stolz, G. (2016). Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. European Mathematical Society. https://doi.org/10.4171/JST/132","ama":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 2016;6(3):557-600. doi:10.4171/JST/132"},"date_updated":"2021-01-12T06:49:12Z","title":"Localization for transversally periodic random potentials on binary trees","department":[{"_id":"LaEr"}],"publist_id":"6112","author":[{"full_name":"Froese, Richard","last_name":"Froese","first_name":"Richard"},{"full_name":"Lee, Darrick","last_name":"Lee","first_name":"Darrick"},{"last_name":"Sadel","orcid":"0000-0001-8255-3968","full_name":"Sadel, Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian"},{"first_name":"Wolfgang","last_name":"Spitzer","full_name":"Spitzer, Wolfgang"},{"first_name":"Günter","last_name":"Stolz","full_name":"Stolz, Günter"}],"_id":"1223","status":"public","type":"journal_article","day":"01","publication":"Journal of Spectral Theory","language":[{"iso":"eng"}],"year":"2016","publication_status":"published","doi":"10.4171/JST/132","volume":6,"date_published":"2016-01-01T00:00:00Z","issue":"3","date_created":"2018-12-11T11:50:48Z","page":"557 - 600","oa_version":"Preprint","abstract":[{"text":"We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, Qr, and a random transversally periodic potential, κQt, with coupling constant κ. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large κ. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing κ. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder.","lang":"eng"}],"month":"01","intvolume":" 6","quality_controlled":"1","scopus_import":1,"publisher":"European Mathematical Society","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1408.3961"}],"oa":1},{"issue":"3","volume":343,"ec_funded":1,"publication_status":"published","file":[{"date_created":"2018-12-12T10:15:02Z","file_name":"IST-2016-703-v1+1_s00220-016-2600-4.pdf","date_updated":"2020-07-14T12:44:42Z","file_size":800792,"creator":"system","checksum":"4fb2411d9c2f56676123165aad46c828","file_id":"5119","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"scopus_import":1,"month":"05","intvolume":" 343","abstract":[{"lang":"eng","text":"We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix (Formula presented.). Focusing on the eigenvalues of (Formula presented.) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required (Formula presented.) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work."}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:44:42Z","date_updated":"2021-01-12T06:49:26Z","ddc":["510","539"],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"703","_id":"1257","page":"881 - 919","date_published":"2016-05-01T00:00:00Z","doi":"10.1007/s00220-016-2600-4","date_created":"2018-12-11T11:50:59Z","has_accepted_license":"1","year":"2016","day":"01","publication":"Communications in Mathematical Physics","quality_controlled":"1","publisher":"Springer","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The work of C. Sadel was supported by NSERC Discovery Grant 92997-2010 RGPIN and by the People Programme (Marie Curie Actions) of the EU 7th Framework Programme FP7/2007-2013, REA Grant 291734.","publist_id":"6067","author":[{"id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian","full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","last_name":"Sadel"},{"first_name":"Bálint","last_name":"Virág","full_name":"Virág, Bálint"}],"article_processing_charge":"Yes (via OA deal)","title":"A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes","citation":{"ista":"Sadel C, Virág B. 2016. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 343(3), 881–919.","chicago":"Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s00220-016-2600-4.","ieee":"C. Sadel and B. Virág, “A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes,” Communications in Mathematical Physics, vol. 343, no. 3. Springer, pp. 881–919, 2016.","short":"C. Sadel, B. Virág, Communications in Mathematical Physics 343 (2016) 881–919.","apa":"Sadel, C., & Virág, B. (2016). A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2600-4","ama":"Sadel C, Virág B. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 2016;343(3):881-919. doi:10.1007/s00220-016-2600-4","mla":"Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications in Mathematical Physics, vol. 343, no. 3, Springer, 2016, pp. 881–919, doi:10.1007/s00220-016-2600-4."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}]}]