[{"day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2024-02-01T00:00:00Z","publication":"Annals of Applied Probability","citation":{"mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","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","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","apa":"Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2000"},"article_type":"original","page":"1623-1662","abstract":[{"lang":"eng","text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble."}],"issue":"1B","type":"journal_article","oa_version":"Preprint","_id":"15025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","status":"public","intvolume":" 34","month":"02","publication_identifier":{"issn":["1050-5164"]},"doi":"10.1214/23-AAP2000","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2208.12206","open_access":"1"}],"external_id":{"arxiv":["2208.12206"]},"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"ec_funded":1,"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"McKenna, Benjamin","id":"b0cc634c-d549-11ee-96c8-87338c7ad808","orcid":"0000-0003-2625-495X","first_name":"Benjamin","last_name":"McKenna"}],"date_created":"2024-02-25T23:00:56Z","date_updated":"2024-02-27T08:29:05Z","volume":34,"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.","year":"2024","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2106.10200"],"isi":["000830344500001"]},"quality_controlled":"1","isi":1,"doi":"10.1007/s00440-022-01156-7","language":[{"iso":"eng"}],"month":"04","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"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).","year":"2023","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"date_updated":"2023-08-14T12:48:09Z","date_created":"2022-08-07T22:02:00Z","volume":185,"file_date_updated":"2023-08-14T12:47:32Z","publication":"Probability Theory and Related Fields","citation":{"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","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","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","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” Probability Theory and Related Fields, vol. 185. Springer Nature, pp. 1183–1218, 2023.","mla":"Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:10.1007/s00440-022-01156-7.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer Nature, 2023. https://doi.org/10.1007/s00440-022-01156-7."},"article_type":"original","page":"1183–1218","date_published":"2023-04-01T00:00:00Z","scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","_id":"11741","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"status":"public","title":"Quenched universality for deformed Wigner matrices","intvolume":" 185","oa_version":"Published Version","file":[{"file_id":"14054","relation":"main_file","date_updated":"2023-08-14T12:47:32Z","date_created":"2023-08-14T12:47:32Z","success":1,"checksum":"b9247827dae5544d1d19c37abe547abc","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","access_level":"open_access","creator":"dernst","file_size":782278,"content_type":"application/pdf"}],"type":"journal_article","abstract":[{"text":"Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.","lang":"eng"}]},{"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"volume":76,"date_created":"2021-12-05T23:01:41Z","date_updated":"2023-10-04T09:22:55Z","year":"2023","acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","publisher":"Wiley","department":[{"_id":"LaEr"}],"publication_status":"published","ec_funded":1,"file_date_updated":"2023-10-04T09:21:48Z","doi":"10.1002/cpa.22028","language":[{"iso":"eng"}],"oa":1,"tmp":{"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","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"external_id":{"arxiv":["1912.04100"],"isi":["000724652500001"]},"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"month":"05","file":[{"success":1,"checksum":"8346bc2642afb4ccb7f38979f41df5d9","date_created":"2023-10-04T09:21:48Z","date_updated":"2023-10-04T09:21:48Z","file_id":"14388","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":803440,"access_level":"open_access","file_name":"2023_CommPureMathematics_Cipolloni.pdf"}],"oa_version":"Published Version","_id":"10405","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 76","ddc":["510"],"title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","status":"public","issue":"5","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]. "}],"type":"journal_article","date_published":"2023-05-01T00:00:00Z","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 2023;76(5):946-1034. doi:10.1002/cpa.22028","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.","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","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:10.1002/cpa.22028.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 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."},"publication":"Communications on Pure and Applied Mathematics","page":"946-1034","article_type":"original","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"doi":"10.3150/22-BEJ1490","language":[{"iso":"eng"}],"month":"05","publication_identifier":{"issn":["1350-7265"]},"year":"2023","publication_status":"published","publisher":"Bernoulli Society for Mathematical Statistics and Probability","department":[{"_id":"LaEr"}],"author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"date_updated":"2023-10-04T10:21:07Z","date_created":"2023-03-05T23:01:05Z","volume":29,"ec_funded":1,"publication":"Bernoulli","citation":{"ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 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.","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","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.","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.","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079."},"article_type":"original","page":"1063-1079","date_published":"2023-05-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","_id":"12707","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","status":"public","intvolume":" 29","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","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."}],"issue":"2"},{"volume":401,"date_created":"2023-04-02T22:01:11Z","date_updated":"2023-10-04T12:10:31Z","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2023","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.","ec_funded":1,"file_date_updated":"2023-10-04T12:09:18Z","language":[{"iso":"eng"}],"doi":"10.1007/s00220-023-04692-y","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000957343500001"]},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"month":"07","file":[{"creator":"dernst","content_type":"application/pdf","file_size":859967,"access_level":"open_access","file_name":"2023_CommMathPhysics_Cipolloni.pdf","success":1,"checksum":"72057940f76654050ca84a221f21786c","date_created":"2023-10-04T12:09:18Z","date_updated":"2023-10-04T12:09:18Z","file_id":"14397","relation":"main_file"}],"oa_version":"Published Version","intvolume":" 401","status":"public","ddc":["510"],"title":"On the spectral form factor for random matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12792","abstract":[{"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.","lang":"eng"}],"type":"journal_article","date_published":"2023-07-01T00:00:00Z","page":"1665-1700","article_type":"original","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” Communications in Mathematical Physics, vol. 401. Springer Nature, pp. 1665–1700, 2023.","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","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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700."},"publication":"Communications in Mathematical Physics","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1"},{"publication":"Probability Theory and Related Fields","external_id":{"arxiv":["2210.12060"]},"citation":{"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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2023).","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.","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","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields.","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","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."},"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.12060","open_access":"1"}],"quality_controlled":"1","article_type":"original","doi":"10.1007/s00440-023-01229-1","date_published":"2023-09-28T00:00:00Z","language":[{"iso":"eng"}],"scopus_import":"1","month":"09","day":"28","article_processing_charge":"No","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.","_id":"14408","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","status":"public","publication_status":"epub_ahead","title":"Mesoscopic central limit theorem for non-Hermitian random matrices","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"date_created":"2023-10-08T22:01:17Z","date_updated":"2023-10-09T07:19:01Z","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:10.1214/23-ECP516.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 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.","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","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","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"},"publication":"Electronic Communications in Probability","page":"1-13","article_type":"original","abstract":[{"lang":"eng","text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices."}],"type":"journal_article","file":[{"creator":"dernst","file_size":479105,"content_type":"application/pdf","access_level":"open_access","file_name":"2023_ElectCommProbability_Dubach.pdf","success":1,"checksum":"a1c6f0a3e33688fd71309c86a9aad86e","date_updated":"2023-02-27T09:43:27Z","date_created":"2023-02-27T09:43:27Z","file_id":"12692","relation":"main_file"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12683","intvolume":" 28","ddc":["510"],"status":"public","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","publication_identifier":{"eissn":["1083-589X"]},"month":"02","doi":"10.1214/23-ECP516","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2108.13694"],"isi":["000950650200005"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"quality_controlled":"1","isi":1,"ec_funded":1,"file_date_updated":"2023-02-27T09:43:27Z","author":[{"full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","first_name":"Guillaume","last_name":"Dubach"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"}],"volume":28,"date_created":"2023-02-26T23:01:01Z","date_updated":"2023-10-17T12:48:10Z","year":"2023","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.","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published"},{"page":"447-489","article_type":"original","citation":{"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","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.","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","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 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.","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."},"publication":"Annals of Applied Probability","date_published":"2023-02-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","intvolume":" 33","status":"public","title":"Functional central limit theorems for Wigner matrices","_id":"12761","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","issue":"1","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)."}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"quality_controlled":"1","isi":1,"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"language":[{"iso":"eng"}],"doi":"10.1214/22-AAP1820","publication_identifier":{"issn":["1050-5164"]},"month":"02","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","year":"2023","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.","volume":33,"date_updated":"2023-10-17T12:48:52Z","date_created":"2023-03-26T22:01:08Z","author":[{"last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"ec_funded":1},{"citation":{"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.","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","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, 2360005, World Scientific Publishing, 2023, doi:10.1142/s0129055x2360005x.","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."},"publication":"Reviews in Mathematical Physics","article_type":"original","date_published":"2023-10-31T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (in subscription journal)","day":"31","_id":"14542","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Universality in low-dimensional BCS theory","status":"public","oa_version":"Published Version","type":"journal_article","abstract":[{"text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit.","lang":"eng"}],"external_id":{"arxiv":["2301.05621"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1142/S0129055X2360005X"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"quality_controlled":"1","doi":"10.1142/s0129055x2360005x","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"month":"10","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.","year":"2023","publisher":"World Scientific Publishing","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"publication_status":"epub_ahead","author":[{"last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard"},{"full_name":"Roos, Barbara","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","last_name":"Roos","first_name":"Barbara"}],"date_created":"2023-11-15T23:48:14Z","date_updated":"2023-11-20T10:04:38Z","article_number":"2360005 ","ec_funded":1},{"type":"journal_article","issue":"4","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"},{"text":"On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.","lang":"fre"}],"intvolume":" 59","status":"public","title":"Functional CLT for non-Hermitian random matrices","_id":"14667","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","page":"2083-2105","article_type":"original","citation":{"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.","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.","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."},"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","date_published":"2023-11-01T00:00:00Z","ec_funded":1,"department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","year":"2023","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.","volume":59,"date_updated":"2023-12-11T12:36:56Z","date_created":"2023-12-10T23:01:00Z","author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","last_name":"Ji","first_name":"Hong Chang"}],"publication_identifier":{"issn":["0246-0203"]},"month":"11","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.11382"}],"external_id":{"arxiv":["2112.11382"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1214/22-AIHP1304"}]