[{"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publication":"Probability Theory and Related Fields","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)"},"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"day":"01","file":[{"creator":"dernst","file_size":782278,"relation":"main_file","content_type":"application/pdf","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","success":1,"access_level":"open_access","date_created":"2023-08-14T12:47:32Z","checksum":"b9247827dae5544d1d19c37abe547abc","file_id":"14054","date_updated":"2023-08-14T12:47:32Z"}],"arxiv":1,"title":"Quenched universality for deformed Wigner matrices","isi":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"doi":"10.1007/s00440-022-01156-7","quality_controlled":"1","acknowledgement":"The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","year":"2023","_id":"11741","page":"1183–1218","oa_version":"Published Version","type":"journal_article","month":"04","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."}],"date_updated":"2023-08-14T12:48:09Z","volume":185,"date_created":"2022-08-07T22:02:00Z","file_date_updated":"2023-08-14T12:47:32Z","status":"public","external_id":{"arxiv":["2106.10200"],"isi":["000830344500001"]},"intvolume":"       185","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 185. Springer Nature, pp. 1183–1218, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","ama":"Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>","mla":"Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>.","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., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>"},"publication_status":"published","oa":1,"has_accepted_license":"1","ddc":["510"],"date_published":"2023-04-01T00:00:00Z"},{"_id":"14408","year":"2023","acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.","date_created":"2023-10-08T22:01:17Z","type":"journal_article","month":"09","oa_version":"Preprint","abstract":[{"text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator.","lang":"eng"}],"date_updated":"2023-10-09T07:19:01Z","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2023).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>.","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.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>"},"external_id":{"arxiv":["2210.12060"]},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.12060"}],"date_published":"2023-09-28T00:00:00Z","oa":1,"publication_status":"epub_ahead","article_type":"original","article_processing_charge":"No","scopus_import":"1","publication":"Probability Theory and Related Fields","department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Mesoscopic central limit theorem for non-Hermitian random matrices","arxiv":1,"day":"28","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"},{"first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1007/s00440-023-01229-1","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]}},{"date_updated":"2024-01-23T10:56:30Z","abstract":[{"text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.","lang":"eng"}],"oa_version":"Preprint","type":"journal_article","month":"11","page":"2192-2242","date_created":"2024-01-22T08:08:41Z","volume":51,"year":"2023","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.","_id":"14849","publication_status":"published","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.04448","open_access":"1"}],"date_published":"2023-11-01T00:00:00Z","status":"public","external_id":{"arxiv":["2206.04448"]},"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>","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.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>."},"intvolume":"        51","day":"01","author":[{"last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"},{"first_name":"Yuanyuan","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"title":"On the rightmost eigenvalue of non-Hermitian random matrices","arxiv":1,"department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","ec_funded":1,"article_processing_charge":"No","article_type":"original","publication":"The Annals of Probability","publication_identifier":{"issn":["0091-1798"]},"quality_controlled":"1","doi":"10.1214/23-aop1643","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"language":[{"iso":"eng"}],"issue":"6","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"]},{"ddc":["510"],"date_published":"2023-05-01T00:00:00Z","has_accepted_license":"1","publication_status":"published","oa":1,"citation":{"mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>.","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., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>."},"intvolume":"        76","status":"public","external_id":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"date_created":"2021-12-05T23:01:41Z","file_date_updated":"2023-10-04T09:21:48Z","volume":76,"date_updated":"2023-10-04T09:22:55Z","abstract":[{"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]. ","lang":"eng"}],"month":"05","type":"journal_article","oa_version":"Published Version","page":"946-1034","_id":"10405","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.","quality_controlled":"1","doi":"10.1002/cpa.22028","publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"language":[{"iso":"eng"}],"issue":"5","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"},{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385"}],"title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","arxiv":1,"day":"01","file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":803440,"success":1,"file_name":"2023_CommPureMathematics_Cipolloni.pdf","access_level":"open_access","date_created":"2023-10-04T09:21:48Z","checksum":"8346bc2642afb4ccb7f38979f41df5d9","date_updated":"2023-10-04T09:21:48Z","file_id":"14388"}],"author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, 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"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","publication":"Communications on Pure and Applied Mathematics","department":[{"_id":"LaEr"}],"publisher":"Wiley","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"title":"Functional central limit theorems for Wigner matrices","arxiv":1,"day":"01","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"}],"article_processing_charge":"No","ec_funded":1,"scopus_import":"1","article_type":"original","publication":"Annals of Applied Probability","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","doi":"10.1214/22-AAP1820","publication_identifier":{"issn":["1050-5164"]},"language":[{"iso":"eng"}],"issue":"1","isi":1,"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"date_created":"2023-03-26T22:01:08Z","volume":33,"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)."}],"date_updated":"2023-10-17T12:48:52Z","type":"journal_article","oa_version":"Preprint","month":"02","page":"447-489","_id":"12761","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.","main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"date_published":"2023-02-01T00:00:00Z","publication_status":"published","oa":1,"citation":{"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.” <i>Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. 2023;33(1):447-489. doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” <i>Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>."},"intvolume":"        33","external_id":{"isi":["000946432400015"],"arxiv":["2012.13218"]},"status":"public"},{"_id":"12792","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.","year":"2023","volume":401,"file_date_updated":"2023-10-04T12:09:18Z","date_created":"2023-04-02T22:01:11Z","page":"1665-1700","date_updated":"2023-10-04T12:10:31Z","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"}],"oa_version":"Published Version","type":"journal_article","month":"07","intvolume":"       401","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. 2023;401:1665-1700. doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>.","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., &#38; Schröder, D. J. (2023). On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” <i>Communications in Mathematical Physics</i>, vol. 401. Springer Nature, pp. 1665–1700, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700."},"external_id":{"isi":["000957343500001"]},"status":"public","date_published":"2023-07-01T00:00:00Z","ddc":["510"],"publication_status":"published","oa":1,"has_accepted_license":"1","publication":"Communications in Mathematical Physics","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"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","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"title":"On the spectral form factor for random matrices","author":[{"first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, 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","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_size":859967,"creator":"dernst","success":1,"file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_created":"2023-10-04T12:09:18Z","access_level":"open_access","date_updated":"2023-10-04T12:09:18Z","file_id":"14397","checksum":"72057940f76654050ca84a221f21786c"}],"day":"01","isi":1,"language":[{"iso":"eng"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"doi":"10.1007/s00220-023-04692-y","quality_controlled":"1","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]}},{"publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}],"publication":"Journal of Functional Analysis","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","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","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"day":"15","file":[{"date_created":"2022-07-29T07:22:08Z","access_level":"open_access","date_updated":"2022-07-29T07:22:08Z","file_id":"11690","checksum":"b75fdad606ab507dc61109e0907d86c0","content_type":"application/pdf","relation":"main_file","file_size":652573,"creator":"dernst","success":1,"file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf"}],"arxiv":1,"title":"Thermalisation for Wigner matrices","article_number":"109394","isi":1,"language":[{"iso":"eng"}],"issue":"8","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"doi":"10.1016/j.jfa.2022.109394","quality_controlled":"1","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.","year":"2022","_id":"10732","abstract":[{"lang":"eng","text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices."}],"date_updated":"2023-08-02T14:12:35Z","oa_version":"Published Version","month":"04","type":"journal_article","volume":282,"date_created":"2022-02-06T23:01:30Z","file_date_updated":"2022-07-29T07:22:08Z","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"status":"public","intvolume":"       282","citation":{"mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. 2022;282(8). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>."},"publication_status":"published","oa":1,"has_accepted_license":"1","date_published":"2022-04-15T00:00:00Z","ddc":["500"]},{"_id":"11418","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.","year":"2022","volume":50,"date_created":"2022-05-29T22:01:53Z","page":"984-1012","abstract":[{"lang":"eng","text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"date_updated":"2023-08-03T07:16:53Z","oa_version":"Preprint","type":"journal_article","month":"05","intvolume":"        50","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. 2022;50(3):984-1012. doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>"},"external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"status":"public","date_published":"2022-05-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"oa":1,"publication_status":"published","publication":"Annals of Probability","scopus_import":"1","article_processing_charge":"No","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","arxiv":1,"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"day":"01","isi":1,"language":[{"iso":"eng"}],"issue":"3","doi":"10.1214/21-AOP1552","quality_controlled":"1","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]}},{"type":"journal_article","month":"10","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"date_updated":"2023-08-04T09:00:35Z","date_created":"2023-01-12T12:07:30Z","file_date_updated":"2023-01-24T10:02:40Z","volume":10,"year":"2022","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.","_id":"12148","has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2022-10-27T00:00:00Z","ddc":["510"],"status":"public","external_id":{"isi":["000873719200001"]},"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022."},"intvolume":"        10","day":"27","file":[{"file_name":"2022_ForumMath_Cipolloni.pdf","success":1,"file_size":817089,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"12356","date_updated":"2023-01-24T10:02:40Z","checksum":"94a049aeb1eea5497aa097712a73c400","date_created":"2023-01-24T10:02:40Z","access_level":"open_access"}],"author":[{"first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"article_number":"e96","title":"Rank-uniform local law for Wigner matrices","department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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)"},"scopus_import":"1","ec_funded":1,"article_processing_charge":"No","publication":"Forum of Mathematics, Sigma","publication_identifier":{"issn":["2050-5094"]},"quality_controlled":"1","doi":"10.1017/fms.2022.86","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"isi":1},{"arxiv":1,"title":"On the condition number of the shifted real Ginibre ensemble","day":"01","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"article_type":"original","scopus_import":"1","article_processing_charge":"No","publication":"SIAM Journal on Matrix Analysis and Applications","department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","doi":"10.1137/21m1424408","publication_identifier":{"issn":["0895-4798"],"eissn":["1095-7162"]},"issue":"3","language":[{"iso":"eng"}],"keyword":["Analysis"],"date_created":"2023-01-12T12:12:38Z","volume":43,"type":"journal_article","oa_version":"Preprint","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]."}],"date_updated":"2023-01-27T06:56:06Z","page":"1469-1487","_id":"12179","year":"2022","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"date_published":"2022-07-01T00:00:00Z","oa":1,"publication_status":"published","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. 2022;43(3):1469-1487. doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>","mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>.","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.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487."},"intvolume":"        43","status":"public","external_id":{"arxiv":["2105.13719"]}},{"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"isi":1,"issue":"11","language":[{"iso":"eng"}],"doi":"10.1007/s00023-022-01188-8","quality_controlled":"1","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"publication":"Annales Henri Poincaré","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","article_processing_charge":"No","scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"title":"Density of small singular values of the shifted real Ginibre ensemble","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"day":"01","file":[{"creator":"dernst","file_size":1333638,"content_type":"application/pdf","relation":"main_file","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","success":1,"access_level":"open_access","date_created":"2023-01-27T11:06:47Z","checksum":"5582f059feeb2f63e2eb68197a34d7dc","file_id":"12424","date_updated":"2023-01-27T11:06:47Z"}],"intvolume":"        23","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, 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.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","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.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>."},"status":"public","external_id":{"isi":["000796323500001"]},"date_published":"2022-11-01T00:00:00Z","ddc":["510"],"publication_status":"published","oa":1,"has_accepted_license":"1","_id":"12232","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.","year":"2022","volume":23,"date_created":"2023-01-16T09:50:26Z","file_date_updated":"2023-01-27T11:06:47Z","page":"3981-4002","oa_version":"Published Version","type":"journal_article","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."}],"date_updated":"2023-08-04T09:33:52Z"},{"date_published":"2022-10-14T00:00:00Z","ddc":["510","530"],"publication_status":"published","oa":1,"has_accepted_license":"1","intvolume":"        63","citation":{"ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10. AIP Publishing, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. 2022;63(10). doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>"},"status":"public","external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"volume":63,"file_date_updated":"2023-01-30T08:01:10Z","date_created":"2023-01-16T09:52:58Z","type":"journal_article","oa_version":"Published Version","month":"10","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)]. "}],"date_updated":"2023-08-04T09:40:02Z","_id":"12243","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.","year":"2022","doi":"10.1063/5.0104290","quality_controlled":"1","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"isi":1,"issue":"10","language":[{"iso":"eng"}],"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_number":"103303","title":"Directional extremal statistics for Ginibre eigenvalues","arxiv":1,"author":[{"last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"},{"last_name":"Xu","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan"}],"day":"14","file":[{"file_name":"2022_JourMathPhysics_Cipolloni2.pdf","success":1,"creator":"dernst","file_size":7356807,"relation":"main_file","content_type":"application/pdf","checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436","date_updated":"2023-01-30T08:01:10Z","access_level":"open_access","date_created":"2023-01-30T08:01:10Z"}],"publication":"Journal of Mathematical Physics","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)"},"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"publisher":"AIP Publishing","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}]},{"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"file":[{"success":1,"file_name":"2022_ElecJournProbability_Cipolloni.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":502149,"checksum":"bb647b48fbdb59361210e425c220cdcb","date_updated":"2023-01-30T11:59:21Z","file_id":"12464","access_level":"open_access","date_created":"2023-01-30T11:59:21Z"}],"day":"12","title":"Optimal multi-resolvent local laws for Wigner matrices","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication":"Electronic Journal of Probability","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","scopus_import":"1","ec_funded":1,"article_processing_charge":"No","publication_identifier":{"eissn":["1083-6489"]},"doi":"10.1214/22-ejp838","quality_controlled":"1","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"isi":1,"language":[{"iso":"eng"}],"page":"1-38","oa_version":"Published Version","type":"journal_article","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."}],"date_updated":"2023-08-04T10:32:23Z","volume":27,"date_created":"2023-01-16T10:04:38Z","file_date_updated":"2023-01-30T11:59:21Z","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.","year":"2022","_id":"12290","oa":1,"publication_status":"published","has_accepted_license":"1","date_published":"2022-09-12T00:00:00Z","ddc":["510"],"status":"public","external_id":{"isi":["000910863700003"]},"intvolume":"        27","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, 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. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38."}},{"isi":1,"language":[{"iso":"eng"}],"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"}],"doi":"10.1007/s00440-020-01003-7","quality_controlled":"1","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"publication":"Probability Theory and Related Fields","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"scopus_import":"1","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","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"arxiv":1,"title":"Edge universality for non-Hermitian random matrices","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, 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"},{"first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"day":"01","file":[{"success":1,"file_name":"2020_ProbTheory_Cipolloni.pdf","relation":"main_file","content_type":"application/pdf","file_size":497032,"creator":"dernst","date_updated":"2020-10-05T14:53:40Z","file_id":"8612","checksum":"611ae28d6055e1e298d53a57beb05ef4","date_created":"2020-10-05T14:53:40Z","access_level":"open_access"}],"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>","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,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>."},"status":"public","external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"date_published":"2021-02-01T00:00:00Z","ddc":["510"],"oa":1,"publication_status":"published","has_accepted_license":"1","_id":"8601","year":"2021","file_date_updated":"2020-10-05T14:53:40Z","date_created":"2020-10-04T22:01:37Z","date_updated":"2024-03-07T15:07:53Z","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."}],"type":"journal_article","month":"02","oa_version":"Published Version"},{"_id":"9412","year":"2021","file_date_updated":"2021-05-25T13:24:19Z","date_created":"2021-05-23T22:01:44Z","volume":26,"oa_version":"Published Version","month":"03","type":"journal_article","date_updated":"2023-08-08T13:39:19Z","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"}],"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-EJP591\">https://doi.org/10.1214/21-EJP591</a>","mla":"Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” <i>Electronic Journal of Probability</i>, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-EJP591\">10.1214/21-EJP591</a>.","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.","ama":"Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href=\"https://doi.org/10.1214/21-EJP591\">10.1214/21-EJP591</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/21-EJP591\">https://doi.org/10.1214/21-EJP591</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” <i>Electronic Journal of Probability</i>, vol. 26. Institute of Mathematical Statistics, 2021."},"intvolume":"        26","external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"status":"public","date_published":"2021-03-23T00:00:00Z","ddc":["510"],"has_accepted_license":"1","publication_status":"published","oa":1,"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)"},"ec_funded":1,"scopus_import":"1","article_processing_charge":"No","publication":"Electronic Journal of Probability","department":[{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Mathematical Statistics","article_number":"24","title":"Fluctuation around the circular law for random matrices with real entries","arxiv":1,"day":"23","file":[{"creator":"kschuh","relation":"main_file","content_type":"application/pdf","file_size":865148,"success":1,"file_name":"2021_EJP_Cipolloni.pdf","access_level":"open_access","date_created":"2021-05-25T13:24:19Z","checksum":"864ab003ad4cffea783f65aa8c2ba69f","date_updated":"2021-05-25T13:24:19Z","file_id":"9423"}],"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"language":[{"iso":"eng"}],"isi":1,"project":[{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385"}],"quality_controlled":"1","doi":"10.1214/21-EJP591","publication_identifier":{"eissn":["10836489"]}},{"external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"status":"public","intvolume":"       388","citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. 2021;388(2):1005–1048. doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021."},"publication_status":"published","oa":1,"has_accepted_license":"1","ddc":["510"],"date_published":"2021-10-29T00:00:00Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","year":"2021","_id":"10221","page":"1005–1048","type":"journal_article","month":"10","oa_version":"Published Version","date_updated":"2023-08-14T10:29:49Z","abstract":[{"lang":"eng","text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020)."}],"volume":388,"file_date_updated":"2022-02-02T10:19:55Z","date_created":"2021-11-07T23:01:25Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"isi":1,"issue":"2","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"doi":"10.1007/s00220-021-04239-z","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication":"Communications in Mathematical Physics","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","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"file":[{"relation":"main_file","content_type":"application/pdf","file_size":841426,"creator":"cchlebak","success":1,"file_name":"2021_CommunMathPhys_Cipolloni.pdf","date_created":"2022-02-02T10:19:55Z","access_level":"open_access","date_updated":"2022-02-02T10:19:55Z","file_id":"10715","checksum":"a2c7b6f5d23b5453cd70d1261272283b"}],"day":"29","title":"Eigenstate thermalization hypothesis for Wigner matrices","arxiv":1},{"volume":48,"date_created":"2019-03-28T09:20:08Z","page":"963-1001","date_updated":"2024-02-22T14:34:33Z","abstract":[{"lang":"eng","text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models."}],"month":"03","oa_version":"Preprint","type":"journal_article","_id":"6184","year":"2020","date_published":"2020-03-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"publication_status":"published","oa":1,"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"},{"relation":"dissertation_contains","id":"6179","status":"public"}]},"intvolume":"        48","citation":{"short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” <i>Annals of Probability</i>, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2020. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>.","ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>.","apa":"Alt, J., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. 2020;48(2):963-1001. doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>"},"external_id":{"isi":["000528269100013"],"arxiv":["1804.07744"]},"status":"public","title":"Correlated random matrices: Band rigidity and edge universality","arxiv":1,"author":[{"last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"day":"01","publication":"Annals of Probability","scopus_import":"1","article_processing_charge":"No","ec_funded":1,"article_type":"original","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"doi":"10.1214/19-AOP1379","quality_controlled":"1","publication_identifier":{"issn":["0091-1798"]},"isi":1,"language":[{"iso":"eng"}],"issue":"2","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]},{"language":[{"iso":"eng"}],"isi":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","doi":"10.1007/s00220-019-03657-4","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_processing_charge":"Yes (via OA deal)","ec_funded":1,"scopus_import":"1","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","publication":"Communications in Mathematical Physics","department":[{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","arxiv":1,"title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","day":"01","file":[{"checksum":"c3a683e2afdcea27afa6880b01e53dc2","file_id":"8771","date_updated":"2020-11-18T11:14:37Z","access_level":"open_access","date_created":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","success":1,"creator":"dernst","file_size":2904574,"content_type":"application/pdf","relation":"main_file"}],"author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"citation":{"ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. 2020;378:1203-1278. doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278."},"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"intvolume":"       378","external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"status":"public","date_published":"2020-09-01T00:00:00Z","ddc":["530","510"],"has_accepted_license":"1","publication_status":"published","oa":1,"_id":"6185","year":"2020","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","date_created":"2019-03-28T10:21:15Z","file_date_updated":"2020-11-18T11:14:37Z","volume":378,"abstract":[{"text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).","lang":"eng"}],"date_updated":"2023-09-07T12:54:12Z","month":"09","oa_version":"Published Version","type":"journal_article","page":"1203-1278"},{"intvolume":"         1","citation":{"mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. 2020;1(1):101-146. doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>."},"external_id":{"arxiv":["1908.01653"]},"status":"public","date_published":"2020-11-16T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"publication_status":"published","oa":1,"_id":"15063","acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","year":"2020","volume":1,"date_created":"2024-03-04T10:27:57Z","page":"101-146","date_updated":"2024-03-04T10:33:15Z","abstract":[{"lang":"eng","text":"We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395)."}],"type":"journal_article","month":"11","oa_version":"Preprint","keyword":["General Medicine"],"language":[{"iso":"eng"}],"issue":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"doi":"10.2140/pmp.2020.1.101","quality_controlled":"1","publication_identifier":{"issn":["2690-1005","2690-0998"]},"publication":"Probability and Mathematical Physics","article_processing_charge":"No","scopus_import":"1","ec_funded":1,"article_type":"original","publisher":"Mathematical Sciences Publishers","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"arxiv":1,"title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"day":"16"},{"article_processing_charge":"No","ec_funded":1,"department":[{"_id":"LaEr"}],"publisher":"Institute of Science and Technology Austria","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","degree_awarded":"PhD","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","file":[{"date_updated":"2020-07-14T12:47:21Z","file_id":"6180","checksum":"6926f66f28079a81c4937e3764be00fc","date_created":"2019-03-28T08:53:52Z","access_level":"closed","file_name":"2019_Schroeder_Thesis.tar.gz","content_type":"application/x-gzip","relation":"source_file","file_size":7104482,"creator":"dernst"},{"file_id":"6181","date_updated":"2020-07-14T12:47:21Z","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","date_created":"2019-03-28T08:53:52Z","access_level":"open_access","file_name":"2019_Schroeder_Thesis.pdf","file_size":4228794,"relation":"main_file","content_type":"application/pdf","creator":"dernst"}],"day":"18","author":[{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"language":[{"iso":"eng"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"}],"doi":"10.15479/AT:ISTA:th6179","publication_identifier":{"issn":["2663-337X"]},"_id":"6179","year":"2019","date_created":"2019-03-28T08:58:59Z","file_date_updated":"2020-07-14T12:47:21Z","type":"dissertation","month":"03","oa_version":"Published Version","abstract":[{"text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure.","lang":"eng"}],"date_updated":"2024-02-22T14:34:33Z","page":"375","citation":{"short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. <a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">https://doi.org/10.15479/AT:ISTA:th6179</a>.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","mla":"Schröder, Dominik J. <i>From Dyson to Pearcey: Universal Statistics in Random Matrix Theory</i>. Institute of Science and Technology Austria, 2019, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">10.15479/AT:ISTA:th6179</a>.","apa":"Schröder, D. J. (2019). <i>From Dyson to Pearcey: Universal statistics in random matrix theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">https://doi.org/10.15479/AT:ISTA:th6179</a>","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">10.15479/AT:ISTA:th6179</a>"},"related_material":{"record":[{"status":"public","id":"1144","relation":"part_of_dissertation"},{"id":"6186","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"6185","status":"public"},{"relation":"part_of_dissertation","id":"6182","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"1012"},{"status":"public","id":"6184","relation":"part_of_dissertation"}]},"status":"public","alternative_title":["ISTA Thesis"],"ddc":["515","519"],"date_published":"2019-03-18T00:00:00Z","supervisor":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","publication_status":"published","oa":1}]