[{"date_created":"2024-02-25T23:00:56Z","doi":"10.1214/23-AAP2000","date_published":"2024-02-01T00:00:00Z","page":"1623-1662","publication":"Annals of Applied Probability","day":"01","year":"2024","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","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.","title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","external_id":{"arxiv":["2208.12206"]},"article_processing_charge":"No","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"b0cc634c-d549-11ee-96c8-87338c7ad808","first_name":"Benjamin","last_name":"McKenna","orcid":"0000-0003-2625-495X","full_name":"McKenna, Benjamin"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","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.","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","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","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.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 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."},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"ec_funded":1,"issue":"1B","volume":34,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"intvolume":" 34","month":"02","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2208.12206"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"LaEr"}],"date_updated":"2024-02-27T08:29:05Z","status":"public","type":"journal_article","article_type":"original","_id":"15025"},{"department":[{"_id":"LaEr"}],"file_date_updated":"2023-08-14T12:47:32Z","ddc":["510"],"date_updated":"2023-08-14T12:48:09Z","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":"11741","volume":185,"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"b9247827dae5544d1d19c37abe547abc","file_id":"14054","file_size":782278,"date_updated":"2023-08-14T12:47:32Z","creator":"dernst","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","date_created":"2023-08-14T12:47:32Z"}],"publication_status":"published","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"intvolume":" 185","month":"04","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"title":"Quenched universality for deformed Wigner matrices","external_id":{"arxiv":["2106.10200"],"isi":["000830344500001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","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"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","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.","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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218."},"date_created":"2022-08-07T22:02:00Z","doi":"10.1007/s00440-022-01156-7","date_published":"2023-04-01T00:00:00Z","page":"1183–1218","publication":"Probability Theory and Related Fields","day":"01","year":"2023","has_accepted_license":"1","isi":1,"oa":1,"quality_controlled":"1","publisher":"Springer Nature","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)."},{"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]. "}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 76","month":"05","publication_status":"published","publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2023_CommPureMathematics_Cipolloni.pdf","date_created":"2023-10-04T09:21:48Z","creator":"dernst","file_size":803440,"date_updated":"2023-10-04T09:21:48Z","success":1,"file_id":"14388","checksum":"8346bc2642afb4ccb7f38979f41df5d9","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"ec_funded":1,"volume":76,"issue":"5","_id":"10405","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"},"article_type":"original","type":"journal_article","status":"public","date_updated":"2023-10-04T09:22:55Z","ddc":["510"],"file_date_updated":"2023-10-04T09:21:48Z","department":[{"_id":"LaEr"}],"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.","oa":1,"publisher":"Wiley","quality_controlled":"1","year":"2023","isi":1,"has_accepted_license":"1","publication":"Communications on Pure and Applied Mathematics","day":"01","page":"946-1034","date_created":"2021-12-05T23:01:41Z","doi":"10.1002/cpa.22028","date_published":"2023-05-01T00:00:00Z","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"}],"citation":{"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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1912.04100"],"isi":["000724652500001"]},"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","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"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices"},{"title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"full_name":"Xu, Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"article_processing_charge":"No","external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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","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","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.","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."},"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"date_published":"2023-05-01T00:00:00Z","doi":"10.3150/22-BEJ1490","date_created":"2023-03-05T23:01:05Z","page":"1063-1079","day":"01","publication":"Bernoulli","isi":1,"year":"2023","publisher":"Bernoulli Society for Mathematical Statistics and Probability","quality_controlled":"1","oa":1,"department":[{"_id":"LaEr"}],"date_updated":"2023-10-04T10:21:07Z","status":"public","type":"journal_article","article_type":"original","_id":"12707","volume":29,"issue":"2","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1350-7265"]},"publication_status":"published","month":"05","intvolume":" 29","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"oa_version":"Preprint","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"}]},{"date_published":"2023-07-01T00:00:00Z","doi":"10.1007/s00220-023-04692-y","date_created":"2023-04-02T22:01:11Z","page":"1665-1700","day":"01","publication":"Communications in Mathematical Physics","has_accepted_license":"1","isi":1,"year":"2023","quality_controlled":"1","publisher":"Springer Nature","oa":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.","title":"On the spectral form factor for random matrices","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","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"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":["000957343500001"]},"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","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","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"},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"volume":401,"ec_funded":1,"file":[{"success":1,"file_id":"14397","checksum":"72057940f76654050ca84a221f21786c","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_created":"2023-10-04T12:09:18Z","creator":"dernst","file_size":859967,"date_updated":"2023-10-04T12:09:18Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"publication_status":"published","month":"07","intvolume":" 401","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."}],"file_date_updated":"2023-10-04T12:09:18Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-10-04T12:10:31Z","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":"12792"},{"article_type":"original","type":"journal_article","status":"public","_id":"14408","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","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"}],"article_processing_charge":"No","external_id":{"arxiv":["2210.12060"]},"department":[{"_id":"LaEr"}],"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","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.","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","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)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","quality_controlled":"1","scopus_import":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.12060"}],"month":"09","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 01+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","volume":28,"ec_funded":1,"publication_identifier":{"eissn":["1083-589X"]},"publication_status":"published","file":[{"success":1,"file_id":"12692","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2023_ElectCommProbability_Dubach.pdf","date_created":"2023-02-27T09:43:27Z","file_size":479105,"date_updated":"2023-02-27T09:43:27Z","creator":"dernst"}],"language":[{"iso":"eng"}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"author":[{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"article_processing_charge":"No","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","citation":{"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.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","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","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","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi: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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","page":"1-13","doi":"10.1214/23-ECP516","date_published":"2023-02-08T00:00:00Z","date_created":"2023-02-26T23:01:01Z","has_accepted_license":"1","isi":1,"year":"2023","day":"08","publication":"Electronic Communications in Probability"},{"abstract":[{"lang":"eng","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)."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.13218"}],"scopus_import":"1","intvolume":" 33","month":"02","publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"1","volume":33,"_id":"12761","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-10-17T12:48:52Z","department":[{"_id":"LaEr"}],"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.","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","year":"2023","isi":1,"publication":"Annals of Applied Probability","day":"01","page":"447-489","date_created":"2023-03-26T22:01:08Z","doi":"10.1214/22-AAP1820","date_published":"2023-02-01T00:00:00Z","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"citation":{"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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.","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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"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"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"title":"Functional central limit theorems for Wigner matrices"},{"_id":"14542","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":"2023-11-20T10:04:38Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1142/S0129055X2360005X"}],"scopus_import":"1","month":"10","publication_status":"epub_ahead","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"language":[{"iso":"eng"}],"ec_funded":1,"article_number":"2360005 ","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"},{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"citation":{"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.","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005.","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.","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","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics. World Scientific Publishing, 2023.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (in subscription journal)","external_id":{"arxiv":["2301.05621"]},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen"},{"last_name":"Roos","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara"}],"title":"Universality in low-dimensional BCS theory","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.","oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","year":"2023","has_accepted_license":"1","publication":"Reviews in Mathematical Physics","day":"31","date_created":"2023-11-15T23:48:14Z","date_published":"2023-10-31T00:00:00Z","doi":"10.1142/s0129055x2360005x"},{"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.","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","year":"2023","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"01","page":"2083-2105","date_created":"2023-12-10T23:01:00Z","doi":"10.1214/22-AIHP1304","date_published":"2023-11-01T00:00:00Z","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"citation":{"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.","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","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","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["2112.11382"]},"author":[{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ji","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang"}],"title":"Functional CLT for non-Hermitian random matrices","abstract":[{"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. ","lang":"eng"},{"lang":"fre","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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.11382"}],"scopus_import":"1","intvolume":" 59","month":"11","publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":59,"issue":"4","_id":"14667","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-12-11T12:36:56Z","department":[{"_id":"LaEr"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","short":"S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023).","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","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."},"title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","author":[{"first_name":"Shoki","last_name":"Sugimoto","full_name":"Sugimoto, Shoki"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"full_name":"Riabov, Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"external_id":{"arxiv":["2304.04213"],"isi":["001035677200002"]},"article_processing_charge":"Yes (in subscription journal)","article_number":"128","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"day":"21","publication":"Journal of Statistical Physics","isi":1,"has_accepted_license":"1","year":"2023","doi":"10.1007/s10955-023-03132-4","date_published":"2023-07-21T00:00:00Z","date_created":"2023-07-30T22:01:02Z","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.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"ddc":["510","530"],"date_updated":"2023-12-13T11:38:44Z","department":[{"_id":"LaEr"}],"file_date_updated":"2023-07-31T07:49:31Z","_id":"13317","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)"},"file":[{"checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","file_id":"13325","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2023-07-31T07:49:31Z","file_name":"2023_JourStatPhysics_Sugimoto.pdf","date_updated":"2023-07-31T07:49:31Z","file_size":612755,"creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"publication_status":"published","issue":"7","volume":190,"ec_funded":1,"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"}],"month":"07","intvolume":" 190","scopus_import":"1"},{"citation":{"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.","ista":"Campbell AJ, O’Rourke S. 2023. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability.","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.","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability (2023).","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” Journal of Theoretical Probability. Springer Nature, 2023.","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","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Campbell","full_name":"Campbell, Andrew J","first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"full_name":"O’Rourke, Sean","last_name":"O’Rourke","first_name":"Sean"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"title":"Spectrum of Lévy–Khintchine random laplacian matrices","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).","quality_controlled":"1","publisher":"Springer Nature","oa":1,"has_accepted_license":"1","isi":1,"year":"2023","day":"26","publication":"Journal of Theoretical Probability","doi":"10.1007/s10959-023-01275-4","date_published":"2023-07-26T00:00:00Z","date_created":"2023-08-06T22:01:13Z","_id":"13975","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":"2023-12-13T12:00:50Z","ddc":["510"],"department":[{"_id":"LaEr"}],"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1007/s10959-023-01275-4","open_access":"1"}],"month":"07","publication_identifier":{"issn":["0894-9840"],"eissn":["1572-9230"]},"publication_status":"epub_ahead","language":[{"iso":"eng"}]},{"ddc":["510"],"date_updated":"2023-12-13T12:24:23Z","file_date_updated":"2023-09-20T11:09:35Z","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"_id":"14343","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","language":[{"iso":"eng"}],"file":[{"file_id":"14352","checksum":"eb747420e6a88a7796fa934151957676","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","creator":"dernst","date_updated":"2023-09-20T11:09:35Z","file_size":852652}],"publication_status":"published","publication_identifier":{"eissn":["2050-5094"]},"ec_funded":1,"volume":11,"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"intvolume":" 11","month":"08","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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.","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","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","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)."},"title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","article_processing_charge":"Yes","external_id":{"arxiv":["2301.05181"],"isi":["001051980200001"]},"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"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","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","first_name":"Oleksii"}],"article_number":"e74","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication":"Forum of Mathematics, Sigma","day":"23","year":"2023","isi":1,"has_accepted_license":"1","date_created":"2023-09-17T22:01:09Z","date_published":"2023-08-23T00:00:00Z","doi":"10.1017/fms.2023.70","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.","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1"},{"article_number":"445201","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"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","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Roderich","last_name":"Tumulka","full_name":"Tumulka, Roderich"}],"external_id":{"isi":["001080908000001"],"arxiv":["2211.16606"]},"article_processing_charge":"Yes (via OA deal)","acknowledgement":"J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331.","publisher":"IOP Publishing","quality_controlled":"1","oa":1,"day":"11","publication":"Journal of Physics A: Mathematical and Theoretical","has_accepted_license":"1","isi":1,"year":"2023","date_published":"2023-10-11T00:00:00Z","doi":"10.1088/1751-8121/acfe62","date_created":"2023-10-12T12:42:53Z","_id":"14421","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":"2023-12-13T13:01:25Z","file_date_updated":"2023-10-16T07:07:24Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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)."}],"month":"10","intvolume":" 56","scopus_import":"1","file":[{"date_created":"2023-10-16T07:07:24Z","file_name":"2023_JourPhysics_Henheik.pdf","creator":"dernst","date_updated":"2023-10-16T07:07:24Z","file_size":721399,"file_id":"14429","checksum":"5b68de147dd4c608b71a6e0e844d2ce9","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"publication_status":"published","issue":"44","volume":56,"ec_funded":1},{"abstract":[{"lang":"eng","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. "}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2010.16083"}],"scopus_import":"1","intvolume":" 33","month":"08","publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":33,"issue":"4","_id":"14750","type":"journal_article","article_type":"original","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"status":"public","date_updated":"2024-01-09T08:16:41Z","department":[{"_id":"LaEr"}],"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,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","year":"2023","publication":"The Annals of Applied Probability","day":"01","page":"2981-3009","date_created":"2024-01-08T13:03:18Z","date_published":"2023-08-01T00:00:00Z","doi":"10.1214/22-aap1882","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"citation":{"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.","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.","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2010.16083"]},"article_processing_charge":"No","author":[{"last_name":"Ding","full_name":"Ding, Xiucai","first_name":"Xiucai"},{"last_name":"Ji","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang"}],"title":"Local laws for multiplication of random matrices"},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"author":[{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu"}],"external_id":{"arxiv":["2108.02728"],"isi":["000946432400021"]},"article_processing_charge":"No","title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","citation":{"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.","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.","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","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"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.","page":"677-725","doi":"10.1214/22-aap1826","date_published":"2023-02-01T00:00:00Z","date_created":"2024-01-10T09:23:31Z","isi":1,"year":"2023","day":"01","publication":"The Annals of Applied Probability","article_type":"original","type":"journal_article","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"_id":"14775","department":[{"_id":"LaEr"}],"date_updated":"2024-01-10T13:31:46Z","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.02728","open_access":"1"}],"month":"02","intvolume":" 33","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"}],"oa_version":"Preprint","issue":"1","volume":33,"ec_funded":1,"publication_identifier":{"issn":["1050-5164"]},"publication_status":"published","language":[{"iso":"eng"}]},{"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","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.","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.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60."},"title":"Spiked multiplicative random matrices and principal components","article_processing_charge":"Yes (in subscription journal)","external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"author":[{"last_name":"Ding","full_name":"Ding, Xiucai","first_name":"Xiucai"},{"full_name":"Ji, Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang"}],"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.","oa":1,"publisher":"Elsevier","quality_controlled":"1","publication":"Stochastic Processes and their Applications","day":"01","year":"2023","isi":1,"has_accepted_license":"1","date_created":"2024-01-10T09:29:25Z","date_published":"2023-09-01T00:00:00Z","doi":"10.1016/j.spa.2023.05.009","page":"25-60","_id":"14780","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"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":["510"],"date_updated":"2024-01-16T08:49:51Z","file_date_updated":"2024-01-16T08:47:31Z","department":[{"_id":"LaEr"}],"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"}],"intvolume":" 163","month":"09","language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2024-01-16T08:47:31Z","file_size":1870349,"date_created":"2024-01-16T08:47:31Z","file_name":"2023_StochasticProcAppl_Ding.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"14806","checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","success":1}],"publication_status":"published","publication_identifier":{"issn":["0304-4149"],"eissn":["1879-209X"]},"ec_funded":1,"volume":163},{"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.","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"day":"01","publication":"The Annals of Probability","year":"2023","date_published":"2023-11-01T00:00:00Z","doi":"10.1214/23-aop1643","date_created":"2024-01-22T08:08:41Z","page":"2192-2242","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":{"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.","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.","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.","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.","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","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 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All terms in the expansion are universal.","lang":"eng"}],"month":"11","intvolume":" 51","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.04448","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0091-1798"]},"publication_status":"published","volume":51,"issue":"6","ec_funded":1,"_id":"14849","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"type":"journal_article","article_type":"original","date_updated":"2024-01-23T10:56:30Z","department":[{"_id":"LaEr"}]},{"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"}],"doi":"10.48550/arXiv.2301.01712","date_published":"2023-01-04T00:00:00Z","ec_funded":1,"date_created":"2024-03-20T09:41:04Z","day":"04","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","year":"2023","status":"public","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"type":"preprint","article_number":"2301.01712","_id":"15128","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"title":"Mesoscopic eigenvalue statistics for Wigner-type matrices","author":[{"full_name":"Riabov, Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"}],"article_processing_charge":"No","external_id":{"arxiv":["2301.01712"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, 2301.01712, doi:10.48550/arXiv.2301.01712.","ieee":"V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” arXiv. .","short":"V. Riabov, ArXiv (n.d.).","ama":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. doi:10.48550/arXiv.2301.01712","apa":"Riabov, V. (n.d.). Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. https://doi.org/10.48550/arXiv.2301.01712","chicago":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2301.01712.","ista":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv, 2301.01712."},"date_updated":"2024-03-25T12:48:20Z"},{"article_processing_charge":"No","external_id":{"arxiv":["2105.13719"]},"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","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"}],"title":"On the condition number of the shifted real Ginibre ensemble","citation":{"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","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.","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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1469-1487","date_created":"2023-01-12T12:12:38Z","doi":"10.1137/21m1424408","date_published":"2022-07-01T00:00:00Z","year":"2022","publication":"SIAM Journal on Matrix Analysis and Applications","day":"01","oa":1,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","department":[{"_id":"LaEr"}],"date_updated":"2023-01-27T06:56:06Z","article_type":"original","type":"journal_article","keyword":["Analysis"],"status":"public","_id":"12179","issue":"3","volume":43,"publication_status":"published","publication_identifier":{"eissn":["1095-7162"],"issn":["0895-4798"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"scopus_import":"1","intvolume":" 43","month":"07","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"},{"ec_funded":1,"issue":"1","volume":63,"publication_status":"published","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}],"intvolume":" 63","month":"01","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"}],"oa_version":"Preprint","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_updated":"2023-08-02T13:44:32Z","type":"journal_article","article_type":"original","keyword":["mathematical physics","statistical and nonlinear physics"],"status":"public","_id":"10600","date_created":"2022-01-03T12:19:48Z","date_published":"2022-01-03T00:00:00Z","doi":"10.1063/5.0051632","year":"2022","isi":1,"publication":"Journal of Mathematical Physics","day":"03","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","article_processing_charge":"No","external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","citation":{"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.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.","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.","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","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","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_number":"011901"},{"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","publication_status":"published","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"language":[{"iso":"eng"}],"file":[{"date_updated":"2022-01-19T09:41:14Z","file_size":357547,"creator":"cchlebak","date_created":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","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","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.","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","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","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000744930400001"],"arxiv":["2106.13780"]},"author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, 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":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"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"},{"ec_funded":1,"volume":10,"language":[{"iso":"eng"}],"file":[{"date_updated":"2022-01-19T09:27:43Z","file_size":705323,"creator":"cchlebak","date_created":"2022-01-19T09:27:43Z","file_name":"2022_ForumMathSigma_Henheik.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","success":1}],"publication_status":"published","publication_identifier":{"eissn":["2050-5094"]},"intvolume":" 10","month":"01","oa_version":"Published Version","abstract":[{"lang":"eng","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"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:27:43Z","ddc":["510"],"date_updated":"2023-08-02T13:53:11Z","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)"},"article_type":"original","type":"journal_article","_id":"10643","date_created":"2022-01-18T16:18:51Z","date_published":"2022-01-18T00:00:00Z","doi":"10.1017/fms.2021.80","publication":"Forum of Mathematics, Sigma","day":"18","year":"2022","isi":1,"has_accepted_license":"1","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","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.","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","article_processing_charge":"Yes","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","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","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","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."},"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_number":"e4"},{"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.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"day":"11","publication":"Mathematical Physics, Analysis and Geometry","has_accepted_license":"1","isi":1,"year":"2022","date_published":"2022-01-11T00:00:00Z","doi":"10.1007/s11040-021-09415-0","date_created":"2022-01-13T15:40:53Z","article_number":"3","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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).","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."},"title":"The BCS critical temperature at high density","author":[{"orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"external_id":{"isi":["000741387600001"],"arxiv":["2106.02015"]},"article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","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"}],"month":"01","intvolume":" 25","scopus_import":"1","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"10624","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","creator":"cchlebak","file_size":505804,"date_updated":"2022-01-14T07:27:45Z","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","date_created":"2022-01-14T07:27:45Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"publication_status":"published","issue":"1","volume":25,"ec_funded":1,"_id":"10623","status":"public","keyword":["geometry and topology","mathematical physics"],"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":["514"],"date_updated":"2023-08-02T13:51:52Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-14T07:27:45Z"},{"_id":"10732","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":["500"],"date_updated":"2023-08-02T14:12:35Z","department":[{"_id":"LaEr"}],"file_date_updated":"2022-07-29T07:22:08Z","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"month":"04","intvolume":" 282","scopus_import":"1","file":[{"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","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"b75fdad606ab507dc61109e0907d86c0","file_id":"11690"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"publication_status":"published","issue":"8","volume":282,"article_number":"109394","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 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.","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","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).","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."},"title":"Thermalisation for Wigner matrices","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]},"article_processing_charge":"Yes (via OA deal)","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.","publisher":"Elsevier","quality_controlled":"1","oa":1,"day":"15","publication":"Journal of Functional Analysis","isi":1,"has_accepted_license":"1","year":"2022","date_published":"2022-04-15T00:00:00Z","doi":"10.1016/j.jfa.2022.109394","date_created":"2022-02-06T23:01:30Z"},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"volume":11,"issue":"4","oa_version":"Preprint","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."}],"intvolume":" 11","month":"10","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"scopus_import":"1","date_updated":"2023-08-03T06:32:22Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"_id":"11135","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"status":"public","article_type":"original","type":"journal_article","publication":"Random Matrices: Theory and Applications","day":"01","year":"2022","isi":1,"date_created":"2022-04-08T07:11:12Z","doi":"10.1142/s2010326322500368","date_published":"2022-10-01T00:00:00Z","oa":1,"publisher":"World Scientific","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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","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","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","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.","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.","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."},"title":"On the operator norm of a Hermitian random matrix with correlated entries","external_id":{"arxiv":["2103.03906"],"isi":["000848873800001"]},"article_processing_charge":"No","author":[{"full_name":"Reker, Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana"}],"article_number":"2250036"},{"date_updated":"2023-08-03T06:34:24Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-08-05T06:01:13Z","_id":"11332","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","publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"11726","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_size":1141462,"date_updated":"2022-08-05T06:01:13Z","creator":"dernst","file_name":"2022_CommunMathPhys_Schnelli.pdf","date_created":"2022-08-05T06:01:13Z"}],"ec_funded":1,"volume":393,"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 393","month":"07","citation":{"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.","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.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","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","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000782737200001"],"arxiv":["2102.04330"]},"article_processing_charge":"No","author":[{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2022","isi":1,"has_accepted_license":"1","publication":"Communications in Mathematical Physics","day":"01","page":"839-907","date_created":"2022-04-24T22:01:44Z","date_published":"2022-07-01T00:00:00Z","doi":"10.1007/s00220-022-04377-y","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.","oa":1,"publisher":"Springer Nature","quality_controlled":"1"},{"article_processing_charge":"No","external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"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","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"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","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","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","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","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","date_created":"2022-05-29T22:01:53Z","date_published":"2022-05-01T00:00:00Z","doi":"10.1214/21-AOP1552","year":"2022","isi":1,"publication":"Annals of Probability","day":"01","article_type":"original","type":"journal_article","status":"public","_id":"11418","department":[{"_id":"LaEr"}],"date_updated":"2023-08-03T07:16:53Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"scopus_import":"1","intvolume":" 50","month":"05","abstract":[{"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).","lang":"eng"}],"oa_version":"Preprint","issue":"3","volume":50,"publication_status":"published","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"language":[{"iso":"eng"}]},{"quality_controlled":"1","publisher":"AIP Publishing","oa":1,"acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","date_published":"2022-12-01T00:00:00Z","doi":"10.1063/5.0104675","date_created":"2023-01-08T23:00:53Z","day":"01","publication":"Journal of Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2022","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_number":"122302","title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"full_name":"Tumulka, Roderich","last_name":"Tumulka","first_name":"Roderich"}],"article_processing_charge":"No","external_id":{"isi":["000900748900002"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","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.","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","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.","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."},"month":"12","intvolume":" 63","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"issue":"12","volume":63,"ec_funded":1,"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"}],"publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","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":"12110","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-20T11:58:59Z","ddc":["510"],"date_updated":"2023-08-03T14:12:01Z"},{"date_published":"2022-10-27T00:00:00Z","doi":"10.1017/fms.2022.86","date_created":"2023-01-12T12:07:30Z","isi":1,"has_accepted_license":"1","year":"2022","day":"27","publication":"Forum of Mathematics, Sigma","publisher":"Cambridge University Press","quality_controlled":"1","oa":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.","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","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"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"article_processing_charge":"No","external_id":{"isi":["000873719200001"]},"title":"Rank-uniform local law for Wigner matrices","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","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.","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","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"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_number":"e96","volume":10,"ec_funded":1,"publication_identifier":{"issn":["2050-5094"]},"publication_status":"published","file":[{"creator":"dernst","date_updated":"2023-01-24T10:02:40Z","file_size":817089,"date_created":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400","success":1}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"10","intvolume":" 10","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."}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-24T10:02:40Z","date_updated":"2023-08-04T09:00:35Z","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","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"_id":"12148"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","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.","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."},"title":"On adiabatic theory for extended fermionic lattice systems","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}],"article_processing_charge":"No","external_id":{"isi":["000905776200001"],"arxiv":["2208.12220"]},"article_number":"121101","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"day":"01","publication":"Journal of Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2022","doi":"10.1063/5.0123441","date_published":"2022-12-01T00:00:00Z","date_created":"2023-01-15T23:00:52Z","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,"ddc":["510"],"date_updated":"2023-08-04T09:14:57Z","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T07:10:52Z","_id":"12184","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)"},"file":[{"file_name":"2022_JourMathPhysics_Henheik2.pdf","date_created":"2023-01-27T07:10:52Z","file_size":5251092,"date_updated":"2023-01-27T07:10:52Z","creator":"dernst","success":1,"file_id":"12410","checksum":"213b93750080460718c050e4967cfdb4","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","issue":"12","volume":63,"ec_funded":1,"oa_version":"Published Version","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."}],"month":"12","intvolume":" 63","scopus_import":"1"},{"title":"The isometry group of Wasserstein spaces: The Hilbertian case","author":[{"full_name":"Gehér, György Pál","last_name":"Gehér","first_name":"György Pál"},{"first_name":"Tamás","full_name":"Titkos, Tamás","last_name":"Titkos"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","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.","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."},"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"}],"date_published":"2022-09-18T00:00:00Z","doi":"10.1112/jlms.12676","date_created":"2023-01-16T09:46:13Z","page":"3865-3894","day":"18","publication":"Journal of the London Mathematical Society","isi":1,"year":"2022","publisher":"Wiley","quality_controlled":"1","oa":1,"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). ","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T09:24:17Z","status":"public","keyword":["General Mathematics"],"type":"journal_article","article_type":"original","_id":"12214","volume":106,"issue":"4","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"publication_status":"published","month":"09","intvolume":" 106","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2102.02037"}],"oa_version":"Preprint","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"}]},{"article_processing_charge":"No","external_id":{"isi":["000796323500001"]},"author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"title":"Density of small singular values of the shifted real Ginibre ensemble","citation":{"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.","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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","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","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"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Springer Nature","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.","page":"3981-4002","date_created":"2023-01-16T09:50:26Z","doi":"10.1007/s00023-022-01188-8","date_published":"2022-11-01T00:00:00Z","year":"2022","has_accepted_license":"1","isi":1,"publication":"Annales Henri Poincaré","day":"01","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","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"status":"public","_id":"12232","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T11:06:47Z","date_updated":"2023-08-04T09:33:52Z","ddc":["510"],"scopus_import":"1","intvolume":" 23","month":"11","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","issue":"11","volume":23,"publication_status":"published","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","date_created":"2023-01-27T11:06:47Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12424","checksum":"5582f059feeb2f63e2eb68197a34d7dc"}]},{"_id":"12243","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":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","date_updated":"2023-08-04T09:40:02Z","ddc":["510","530"],"file_date_updated":"2023-01-30T08:01:10Z","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","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)]. "}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 63","month":"10","publication_status":"published","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"language":[{"iso":"eng"}],"file":[{"file_id":"12436","checksum":"2db278ae5b07f345a7e3fec1f92b5c33","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2023-01-30T08:01:10Z","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","date_updated":"2023-01-30T08:01:10Z","file_size":7356807,"creator":"dernst"}],"ec_funded":1,"volume":63,"issue":"10","article_number":"103303","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"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.","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","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","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","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","external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"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"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"title":"Directional extremal statistics for Ginibre eigenvalues","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.","oa":1,"publisher":"AIP Publishing","quality_controlled":"1","year":"2022","has_accepted_license":"1","isi":1,"publication":"Journal of Mathematical Physics","day":"14","date_created":"2023-01-16T09:52:58Z","doi":"10.1063/5.0104290","date_published":"2022-10-14T00:00:00Z"},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_processing_charge":"No","external_id":{"isi":["000910863700003"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"title":"Optimal multi-resolvent local laws for Wigner matrices","citation":{"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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","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","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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","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.","page":"1-38","date_created":"2023-01-16T10:04:38Z","doi":"10.1214/22-ejp838","date_published":"2022-09-12T00:00:00Z","year":"2022","has_accepted_license":"1","isi":1,"publication":"Electronic Journal of Probability","day":"12","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":"12290","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-30T11:59:21Z","date_updated":"2023-08-04T10:32:23Z","ddc":["510"],"scopus_import":"1","intvolume":" 27","month":"09","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."}],"oa_version":"Published Version","ec_funded":1,"volume":27,"publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"12464","checksum":"bb647b48fbdb59361210e425c220cdcb","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"}]},{"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000833007200002"]},"author":[{"orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"title":"The BCS energy gap at high density","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"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_number":"5","date_created":"2022-08-05T11:36:56Z","date_published":"2022-07-29T00:00:00Z","doi":"10.1007/s10955-022-02965-9","year":"2022","isi":1,"has_accepted_license":"1","publication":"Journal of Statistical Physics","day":"29","oa":1,"publisher":"Springer Nature","quality_controlled":"1","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)","file_date_updated":"2022-08-08T07:36:34Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"date_updated":"2023-09-05T14:57:49Z","ddc":["530"],"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","_id":"11732","ec_funded":1,"volume":189,"publication_status":"published","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":419563,"date_updated":"2022-08-08T07:36:34Z","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","date_created":"2022-08-08T07:36:34Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746"}],"scopus_import":"1","intvolume":" 189","month":"07","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."}],"oa_version":"Published Version"},{"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":"10285","department":[{"_id":"LaEr"}],"file_date_updated":"2021-11-15T10:10:17Z","ddc":["519"],"date_updated":"2021-11-15T10:48:46Z","intvolume":" 26","month":"09","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"volume":26,"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","file_size":735940,"date_updated":"2021-11-15T10:10:17Z","file_name":"2021_ElecJournalProb_Dubach.pdf","date_created":"2021-11-15T10:10:17Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"10288","checksum":"1c975afb31460277ce4d22b93538e5f9"}],"publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_number":"124","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","article_processing_charge":"No","author":[{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"short":"G. Dubach, Electronic Journal of Probability 26 (2021).","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686","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","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.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","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."},"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","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.","date_created":"2021-11-14T23:01:25Z","date_published":"2021-09-28T00:00:00Z","doi":"10.1214/21-EJP686","publication":"Electronic Journal of Probability","day":"28","year":"2021","has_accepted_license":"1"},{"day":"08","publication":"arXiv","language":[{"iso":"eng"}],"publication_status":"submitted","year":"2021","doi":"10.48550/arXiv.2103.04817","date_published":"2021-03-08T00:00:00Z","date_created":"2021-03-09T11:08:15Z","ec_funded":1,"oa_version":"Preprint","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.","abstract":[{"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.","lang":"eng"}],"month":"03","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-05-03T10:22:59Z","citation":{"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","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","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","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. .","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.","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.","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."},"department":[{"_id":"LaEr"}],"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","author":[{"first_name":"Louis-Pierre","last_name":"Arguin","full_name":"Arguin, Louis-Pierre"},{"last_name":"Dubach","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"},{"full_name":"Hartung, Lisa","last_name":"Hartung","first_name":"Lisa"}],"article_processing_charge":"No","external_id":{"arxiv":["2103.04817"]},"article_number":"2103.04817","_id":"9230","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"status":"public","type":"preprint"},{"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","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"language":[{"iso":"eng"}],"publication":"arXiv","day":"21","publication_status":"submitted","year":"2021","ec_funded":1,"date_created":"2021-03-23T05:38:48Z","related_material":{"record":[{"relation":"other","id":"9946","status":"public"}]},"doi":"10.48550/arXiv.2103.11389","date_published":"2021-03-21T00:00:00Z","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","citation":{"mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, doi: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. .","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","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."},"date_updated":"2023-05-03T10:26:45Z","title":"Formal verification of Zagier's one-sentence proof","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"article_processing_charge":"No","external_id":{"arxiv":["2103.11389"]},"author":[{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"first_name":"Fabian","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","orcid":"0000-0003-1548-0177","full_name":"Mühlböck, Fabian","last_name":"Mühlböck"}]},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.11678"}],"intvolume":" 609","month":"01","abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","ec_funded":1,"volume":609,"publication_status":"published","publication_identifier":{"issn":["0024-3795"]},"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"status":"public","_id":"8373","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T10:58:14Z","oa":1,"quality_controlled":"1","publisher":"Elsevier","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.","page":"203-217","date_created":"2020-09-11T08:35:50Z","date_published":"2021-01-15T00:00:00Z","doi":"10.1016/j.laa.2020.09.007","year":"2021","isi":1,"publication":"Linear Algebra and its Applications","day":"15","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"external_id":{"isi":["000581730500011"],"arxiv":["2002.11678"]},"article_processing_charge":"No","author":[{"first_name":"József","full_name":"Pitrik, József","last_name":"Pitrik"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","citation":{"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","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","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.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"article_type":"original","type":"journal_article","keyword":["General Mathematics"],"status":"public","_id":"9036","department":[{"_id":"LaEr"}],"date_updated":"2023-08-07T13:34:48Z","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","ec_funded":1,"volume":380,"issue":"3","publication_status":"published","publication_identifier":{"issn":["0001-8708"]},"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"}],"article_number":"107595","external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"article_processing_charge":"No","author":[{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"title":"The metric property of the quantum Jensen-Shannon divergence","citation":{"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","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Elsevier","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.","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"},{"title":"Fluctuation around the circular law for random matrices with real entries","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","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"}],"external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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).","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","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.","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."},"project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"24","date_published":"2021-03-23T00:00:00Z","doi":"10.1214/21-EJP591","date_created":"2021-05-23T22:01:44Z","day":"23","publication":"Electronic Journal of Probability","has_accepted_license":"1","isi":1,"year":"2021","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"file_date_updated":"2021-05-25T13:24:19Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-08T13:39:19Z","status":"public","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":"9412","volume":26,"ec_funded":1,"file":[{"file_size":865148,"date_updated":"2021-05-25T13:24:19Z","creator":"kschuh","file_name":"2021_EJP_Cipolloni.pdf","date_created":"2021-05-25T13:24:19Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_id":"9423"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["10836489"]},"publication_status":"published","month":"03","intvolume":" 26","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","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","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.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","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."},"title":"Equipartition principle for Wigner matrices","external_id":{"arxiv":["2008.07061"],"isi":["000654960800001"]},"article_processing_charge":"No","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","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"}],"article_number":"e44","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publication":"Forum of Mathematics, Sigma","day":"27","year":"2021","isi":1,"has_accepted_license":"1","date_created":"2021-06-13T22:01:33Z","date_published":"2021-05-27T00:00:00Z","doi":"10.1017/fms.2021.38","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","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","ddc":["510"],"date_updated":"2023-08-08T14:03:40Z","department":[{"_id":"LaEr"}],"file_date_updated":"2021-06-15T14:40:45Z","_id":"9550","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","language":[{"iso":"eng"}],"file":[{"checksum":"47c986578de132200d41e6d391905519","file_id":"9555","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2021-06-15T14:40:45Z","file_name":"2021_ForumMath_Bao.pdf","date_updated":"2021-06-15T14:40:45Z","file_size":483458,"creator":"cziletti"}],"publication_status":"published","publication_identifier":{"eissn":["20505094"]},"ec_funded":1,"volume":9,"oa_version":"Published Version","abstract":[{"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. ","lang":"eng"}],"intvolume":" 9","month":"05","scopus_import":"1"},{"publication":"Annales Henri Poincaré ","day":"01","year":"2021","isi":1,"has_accepted_license":"1","date_created":"2021-08-15T22:01:29Z","date_published":"2021-12-01T00:00:00Z","doi":"10.1007/s00023-021-01085-6","page":"4205–4269","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.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","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.","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.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.","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","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","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."},"title":"Scattering in quantum dots via noncommutative rational functions","article_processing_charge":"Yes (in subscription journal)","external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"author":[{"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"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","last_name":"Nemish"}],"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"11365","checksum":"8d6bac0e2b0a28539608b0538a8e3b38","creator":"dernst","file_size":1162454,"date_updated":"2022-05-12T12:50:27Z","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","date_created":"2022-05-12T12:50:27Z"}],"publication_status":"published","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"ec_funded":1,"volume":22,"oa_version":"Published Version","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"}],"intvolume":" 22","month":"12","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-11T10:31:48Z","file_date_updated":"2022-05-12T12:50:27Z","department":[{"_id":"LaEr"}],"_id":"9912","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"},{"oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","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","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"article_processing_charge":"Yes (via OA deal)","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","citation":{"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.","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","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","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","intvolume":" 388","month":"10","abstract":[{"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).","lang":"eng"}],"oa_version":"Published Version","volume":388,"issue":"2","publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2021_CommunMathPhys_Cipolloni.pdf","date_created":"2022-02-02T10:19:55Z","file_size":841426,"date_updated":"2022-02-02T10:19:55Z","creator":"cchlebak","success":1,"file_id":"10715","checksum":"a2c7b6f5d23b5453cd70d1261272283b","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"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":"10221","department":[{"_id":"LaEr"}],"file_date_updated":"2022-02-02T10:19:55Z","date_updated":"2023-08-14T10:29:49Z","ddc":["510"]},{"ec_funded":1,"file":[{"success":1,"file_id":"9043","checksum":"5a93658a5f19478372523ee232887e2b","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"thesis.pdf","date_created":"2021-01-25T14:19:03Z","file_size":4127796,"date_updated":"2021-01-25T14:19:03Z","creator":"gcipollo"},{"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}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","month":"01","alternative_title":["ISTA Thesis"],"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"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2021-01-25T14:19:10Z","ddc":["510"],"supervisor":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"date_updated":"2023-09-07T13:29:32Z","status":"public","type":"dissertation","_id":"9022","date_published":"2021-01-25T00:00:00Z","doi":"10.15479/AT:ISTA:9022","date_created":"2021-01-21T18:16:54Z","page":"380","day":"25","has_accepted_license":"1","year":"2021","publisher":"Institute of Science and Technology Austria","oa":1,"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.","title":"Fluctuations in the spectrum of random matrices","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","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.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","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","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022"},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}]},{"ec_funded":1,"issue":"2","volume":2,"publication_status":"published","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1907.13631"}],"scopus_import":"1","intvolume":" 2","month":"05","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","department":[{"_id":"LaEr"}],"date_updated":"2024-02-19T08:30:00Z","type":"journal_article","article_type":"original","status":"public","_id":"15013","page":"221-280","date_created":"2024-02-18T23:01:03Z","doi":"10.2140/pmp.2021.2.221","date_published":"2021-05-21T00:00:00Z","year":"2021","publication":"Probability and Mathematical Physics","day":"21","oa":1,"publisher":"Mathematical Sciences Publishers","quality_controlled":"1","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.","external_id":{"arxiv":["1907.13631"]},"article_processing_charge":"No","author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","last_name":"Alt"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"}],"title":"Spectral radius of random matrices with independent entries","citation":{"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.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","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.","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","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.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]},{"ec_funded":1,"publication_status":"published","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"language":[{"iso":"eng"}],"file":[{"file_size":497032,"date_updated":"2020-10-05T14:53:40Z","creator":"dernst","file_name":"2020_ProbTheory_Cipolloni.pdf","date_created":"2020-10-05T14:53:40Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"611ae28d6055e1e298d53a57beb05ef4","file_id":"8612"}],"scopus_import":"1","month":"02","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","file_date_updated":"2020-10-05T14:53:40Z","department":[{"_id":"LaEr"}],"date_updated":"2024-03-07T15:07:53Z","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":"8601","date_created":"2020-10-04T22:01:37Z","doi":"10.1007/s00440-020-01003-7","date_published":"2021-02-01T00:00:00Z","year":"2021","isi":1,"has_accepted_license":"1","publication":"Probability Theory and Related Fields","day":"01","oa":1,"quality_controlled":"1","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"title":"Edge universality for non-Hermitian random matrices","citation":{"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","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 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.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"}]},{"doi":"10.1090/tran/8113","date_published":"2020-08-01T00:00:00Z","date_created":"2020-01-29T10:20:46Z","page":"5855-5883","day":"01","publication":"Transactions of the American Mathematical Society","isi":1,"year":"2020","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"title":"Isometric study of Wasserstein spaces - the real line","author":[{"first_name":"Gyorgy Pal","last_name":"Geher","full_name":"Geher, Gyorgy Pal"},{"full_name":"Titkos, Tamas","last_name":"Titkos","first_name":"Tamas"},{"last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"article_processing_charge":"No","external_id":{"isi":["000551418100018"],"arxiv":["2002.00859"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","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.","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","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","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."},"project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"}],"volume":373,"issue":"8","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"publication_status":"published","month":"08","intvolume":" 373","main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"oa_version":"Preprint","abstract":[{"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)).","lang":"eng"}],"department":[{"_id":"LaEr"}],"ddc":["515"],"date_updated":"2023-08-17T14:31:03Z","status":"public","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"article_type":"original","type":"journal_article","_id":"7389"},{"status":"public","type":"journal_article","article_type":"original","_id":"7512","department":[{"_id":"LaEr"}],"date_updated":"2023-08-18T06:36:10Z","month":"07","intvolume":" 278","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11340"}],"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"}],"issue":"12","volume":278,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00221236"],"eissn":["10960783"]},"publication_status":"published","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"article_number":"108507","title":"Local laws for polynomials of Wigner matrices","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"},{"last_name":"Nemish","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","first_name":"Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","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.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","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.","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","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","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."},"quality_controlled":"1","publisher":"Elsevier","oa":1,"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","doi":"10.1016/j.jfa.2020.108507","date_published":"2020-07-01T00:00:00Z","date_created":"2020-02-23T23:00:36Z","day":"01","publication":"Journal of Functional Analysis","isi":1,"year":"2020"}]