[{"month":"02","publication_identifier":{"issn":["1050-5164"]},"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":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"doi":"10.1214/23-AAP2000","language":[{"iso":"eng"}],"ec_funded":1,"year":"2024","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.","publication_status":"published","publisher":"Institute of Mathematical Statistics","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"},{"first_name":"Benjamin","last_name":"McKenna","id":"b0cc634c-d549-11ee-96c8-87338c7ad808","orcid":"0000-0003-2625-495X","full_name":"McKenna, Benjamin"}],"date_created":"2024-02-25T23:00:56Z","date_updated":"2024-02-27T08:29:05Z","volume":34,"scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Annals of Applied Probability","citation":{"chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000.","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.","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.","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","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"},"article_type":"original","page":"1623-1662","date_published":"2024-02-01T00:00:00Z","type":"journal_article","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"}],"issue":"1B","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15025","title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","status":"public","intvolume":" 34","oa_version":"Preprint"},{"scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","publication":"Probability Theory and Related Fields","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.","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.","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."},"article_type":"original","page":"1183–1218","date_published":"2023-04-01T00:00:00Z","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"}],"_id":"11741","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Quenched universality for deformed Wigner matrices","ddc":["510"],"intvolume":" 185","file":[{"access_level":"open_access","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","file_size":782278,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"14054","checksum":"b9247827dae5544d1d19c37abe547abc","success":1,"date_created":"2023-08-14T12:47:32Z","date_updated":"2023-08-14T12:47:32Z"}],"oa_version":"Published Version","month":"04","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"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":["2106.10200"],"isi":["000830344500001"]},"isi":1,"quality_controlled":"1","doi":"10.1007/s00440-022-01156-7","language":[{"iso":"eng"}],"file_date_updated":"2023-08-14T12:47:32Z","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","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"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"}],"date_updated":"2023-08-14T12:48:09Z","date_created":"2022-08-07T22:02:00Z","volume":185},{"ec_funded":1,"file_date_updated":"2023-10-04T09:21:48Z","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.","year":"2023","department":[{"_id":"LaEr"}],"publisher":"Wiley","publication_status":"published","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"volume":76,"date_created":"2021-12-05T23:01:41Z","date_updated":"2023-10-04T09:22:55Z","publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"month":"05","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":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Doctoral Program","call_identifier":"H2020","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","doi":"10.1002/cpa.22028","language":[{"iso":"eng"}],"type":"journal_article","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]. "}],"_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","oa_version":"Published Version","file":[{"creator":"dernst","file_size":803440,"content_type":"application/pdf","access_level":"open_access","file_name":"2023_CommPureMathematics_Cipolloni.pdf","success":1,"checksum":"8346bc2642afb4ccb7f38979f41df5d9","date_created":"2023-10-04T09:21:48Z","date_updated":"2023-10-04T09:21:48Z","file_id":"14388","relation":"main_file"}],"scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","citation":{"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.","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.","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.","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"},"publication":"Communications on Pure and Applied Mathematics","page":"946-1034","article_type":"original","date_published":"2023-05-01T00:00:00Z"},{"article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2023-05-01T00:00:00Z","page":"1063-1079","article_type":"original","citation":{"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","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","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.","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","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."},"publication":"Bernoulli","issue":"2","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."}],"type":"journal_article","oa_version":"Preprint","intvolume":" 29","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","status":"public","_id":"12707","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1350-7265"]},"month":"05","language":[{"iso":"eng"}],"doi":"10.3150/22-BEJ1490","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,"external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"oa":1,"ec_funded":1,"volume":29,"date_created":"2023-03-05T23:01:05Z","date_updated":"2023-10-04T10:21:07Z","author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"department":[{"_id":"LaEr"}],"publisher":"Bernoulli Society for Mathematical Statistics and Probability","publication_status":"published","year":"2023"},{"file_date_updated":"2023-10-04T12:09:18Z","ec_funded":1,"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","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.","date_created":"2023-04-02T22:01:11Z","date_updated":"2023-10-04T12:10:31Z","volume":401,"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"month":"07","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"isi":1,"quality_controlled":"1","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"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"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00220-023-04692-y","type":"journal_article","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"}],"title":"On the spectral form factor for random matrices","status":"public","ddc":["510"],"intvolume":" 401","_id":"12792","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"14397","date_created":"2023-10-04T12:09:18Z","date_updated":"2023-10-04T12:09:18Z","checksum":"72057940f76654050ca84a221f21786c","success":1,"file_name":"2023_CommMathPhysics_Cipolloni.pdf","access_level":"open_access","content_type":"application/pdf","file_size":859967,"creator":"dernst"}],"scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","article_type":"original","page":"1665-1700","publication":"Communications in Mathematical Physics","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 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","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.","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."},"date_published":"2023-07-01T00:00:00Z"}]