[{"month":"04","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"oa":1,"status":"public","_id":"11741","year":"2023","date_updated":"2023-08-14T12:48:09Z","arxiv":1,"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."}],"citation":{"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>","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <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>.","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>","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>."},"intvolume":"       185","ddc":["510"],"file_date_updated":"2023-08-14T12:47:32Z","scopus_import":"1","date_published":"2023-04-01T00:00:00Z","oa_version":"Published Version","publication_status":"published","doi":"10.1007/s00440-022-01156-7","title":"Quenched universality for deformed Wigner matrices","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","content_type":"application/pdf","file_size":782278,"success":1,"checksum":"b9247827dae5544d1d19c37abe547abc","creator":"dernst","file_id":"14054","access_level":"open_access","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","date_updated":"2023-08-14T12:47:32Z","date_created":"2023-08-14T12:47:32Z"}],"isi":1,"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","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).","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"volume":185,"quality_controlled":"1","article_type":"original","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"type":"journal_article","date_created":"2022-08-07T22:02:00Z","page":"1183–1218","publication":"Probability Theory and Related Fields","has_accepted_license":"1"},{"intvolume":"        11","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023.","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>.","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e74, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>"},"ddc":["510"],"scopus_import":"1","file_date_updated":"2023-09-20T11:09:35Z","date_published":"2023-08-23T00:00:00Z","oa_version":"Published Version","publication_status":"published","doi":"10.1017/fms.2023.70","ec_funded":1,"month":"08","oa":1,"publication_identifier":{"eissn":["2050-5094"]},"status":"public","_id":"14343","article_number":"e74","year":"2023","date_updated":"2023-12-13T12:24:23Z","arxiv":1,"abstract":[{"lang":"eng","text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation."}],"external_id":{"arxiv":["2301.05181"],"isi":["001051980200001"]},"quality_controlled":"1","volume":11,"article_processing_charge":"Yes","article_type":"original","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"},{"_id":"GradSch"}],"type":"journal_article","date_created":"2023-09-17T22:01:09Z","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","publisher":"Cambridge University Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","content_type":"application/pdf","file_size":852652,"success":1,"date_updated":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","date_created":"2023-09-20T11:09:35Z","checksum":"eb747420e6a88a7796fa934151957676","creator":"dernst","file_id":"14352","access_level":"open_access"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"isi":1,"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","last_name":"Kolupaiev","first_name":"Oleksii"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"23","acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331."},{"oa":1,"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"status":"public","month":"09","year":"2023","date_updated":"2023-10-09T07:19:01Z","abstract":[{"lang":"eng","text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 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."}],"arxiv":1,"_id":"14408","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.12060","open_access":"1"}],"scopus_import":"1","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields.","apa":"Cipolloni, G., Erdös, L., &#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>","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>.","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>.","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.","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>"},"publication_status":"epub_ahead","doi":"10.1007/s00440-023-01229-1","date_published":"2023-09-28T00:00:00Z","oa_version":"Preprint","title":"Mesoscopic central limit theorem for non-Hermitian random matrices","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"28","acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.","author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"article_type":"original","article_processing_charge":"No","external_id":{"arxiv":["2210.12060"]},"quality_controlled":"1","date_created":"2023-10-08T22:01:17Z","publication":"Probability Theory and Related Fields","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"type":"journal_article"},{"publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the rightmost eigenvalue of non-Hermitian random matrices","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan"}],"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.","day":"01","external_id":{"arxiv":["2206.04448"]},"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"volume":51,"quality_controlled":"1","article_type":"original","article_processing_charge":"No","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"date_created":"2024-01-22T08:08:41Z","page":"2192-2242","publication":"The Annals of Probability","month":"11","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"issn":["0091-1798"]},"_id":"14849","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"}],"arxiv":1,"issue":"6","year":"2023","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <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>","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>.","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>","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>."},"intvolume":"        51","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"oa_version":"Preprint","date_published":"2023-11-01T00:00:00Z","publication_status":"published","doi":"10.1214/23-aop1643"},{"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Communications on Pure and Applied Mathematics","date_created":"2021-12-05T23:01:41Z","page":"946-1034","has_accepted_license":"1","volume":76,"quality_controlled":"1","external_id":{"arxiv":["1912.04100"],"isi":["000724652500001"]},"article_type":"original","article_processing_charge":"Yes (via OA deal)","file":[{"date_created":"2023-10-04T09:21:48Z","date_updated":"2023-10-04T09:21:48Z","file_name":"2023_CommPureMathematics_Cipolloni.pdf","access_level":"open_access","file_id":"14388","checksum":"8346bc2642afb4ccb7f38979f41df5d9","creator":"dernst","file_size":803440,"success":1,"content_type":"application/pdf","relation":"main_file"}],"isi":1,"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"day":"01","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"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.","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Wiley","date_published":"2023-05-01T00:00:00Z","oa_version":"Published Version","doi":"10.1002/cpa.22028","publication_status":"published","citation":{"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.","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>","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>.","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>"},"intvolume":"        76","ddc":["510"],"file_date_updated":"2023-10-04T09:21:48Z","scopus_import":"1","_id":"10405","year":"2023","issue":"5","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"}],"arxiv":1,"date_updated":"2023-10-04T09:22:55Z","ec_funded":1,"month":"05","publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"oa":1,"status":"public"},{"title":"Functional central limit theorems for Wigner matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","day":"01","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.","isi":1,"author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_processing_charge":"No","article_type":"original","volume":33,"quality_controlled":"1","external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"publication":"Annals of Applied Probability","page":"447-489","date_created":"2023-03-26T22:01:08Z","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"issn":["1050-5164"]},"oa":1,"status":"public","ec_funded":1,"month":"02","year":"2023","arxiv":1,"abstract":[{"lang":"eng","text":"We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"issue":"1","date_updated":"2023-10-17T12:48:52Z","_id":"12761","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.13218"}],"scopus_import":"1","intvolume":"        33","citation":{"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>.","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>","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.","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>"},"doi":"10.1214/22-AAP1820","publication_status":"published","date_published":"2023-02-01T00:00:00Z","oa_version":"Preprint"},{"month":"07","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"_id":"12792","date_updated":"2023-10-04T12:10:31Z","abstract":[{"lang":"eng","text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics."}],"year":"2023","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","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>","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.","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>","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>.","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>."},"intvolume":"       401","scopus_import":"1","file_date_updated":"2023-10-04T12:09:18Z","ddc":["510"],"oa_version":"Published Version","date_published":"2023-07-01T00:00:00Z","publication_status":"published","doi":"10.1007/s00220-023-04692-y","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the spectral form factor for random matrices","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"isi":1,"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"file":[{"creator":"dernst","file_id":"14397","checksum":"72057940f76654050ca84a221f21786c","access_level":"open_access","date_updated":"2023-10-04T12:09:18Z","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_created":"2023-10-04T12:09:18Z","content_type":"application/pdf","relation":"main_file","success":1,"file_size":859967}],"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.","day":"01","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"isi":["000957343500001"]},"quality_controlled":"1","volume":401,"article_type":"original","article_processing_charge":"Yes (via OA deal)","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"has_accepted_license":"1","date_created":"2023-04-02T22:01:11Z","page":"1665-1700","publication":"Communications in Mathematical Physics"},{"status":"public","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"oa":1,"month":"04","abstract":[{"text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","lang":"eng"}],"arxiv":1,"issue":"8","date_updated":"2023-08-02T14:12:35Z","year":"2022","article_number":"109394","_id":"10732","scopus_import":"1","file_date_updated":"2022-07-29T07:22:08Z","ddc":["500"],"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>.","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>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <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>.","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.","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>"},"intvolume":"       282","doi":"10.1016/j.jfa.2022.109394","publication_status":"published","oa_version":"Published Version","date_published":"2022-04-15T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Elsevier","title":"Thermalisation for Wigner matrices","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to  for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","day":"15","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"isi":1,"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"file":[{"access_level":"open_access","creator":"dernst","file_id":"11690","checksum":"b75fdad606ab507dc61109e0907d86c0","date_created":"2022-07-29T07:22:08Z","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","date_updated":"2022-07-29T07:22:08Z","success":1,"file_size":652573,"content_type":"application/pdf","relation":"main_file"}],"article_processing_charge":"Yes (via OA deal)","article_type":"original","volume":282,"quality_controlled":"1","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"has_accepted_license":"1","publication":"Journal of Functional Analysis","date_created":"2022-02-06T23:01:30Z","type":"journal_article","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}]},{"month":"05","status":"public","oa":1,"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"_id":"11418","date_updated":"2023-08-03T07:16:53Z","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)."}],"arxiv":1,"issue":"3","year":"2022","citation":{"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>","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","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>","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."},"intvolume":"        50","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"oa_version":"Preprint","date_published":"2022-05-01T00:00:00Z","publication_status":"published","doi":"10.1214/21-AOP1552","publisher":"Institute of Mathematical Statistics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"isi":1,"acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","day":"01","external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"quality_controlled":"1","volume":50,"article_processing_charge":"No","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"page":"984-1012","date_created":"2022-05-29T22:01:53Z","publication":"Annals of Probability"},{"title":"Rank-uniform local law for Wigner matrices","publisher":"Cambridge University Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"27","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.","file":[{"access_level":"open_access","file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400","creator":"dernst","date_created":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","date_updated":"2023-01-24T10:02:40Z","file_size":817089,"success":1,"content_type":"application/pdf","relation":"main_file"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"isi":1,"article_type":"original","article_processing_charge":"No","external_id":{"isi":["000873719200001"]},"volume":10,"quality_controlled":"1","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"date_created":"2023-01-12T12:07:30Z","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"type":"journal_article","publication_identifier":{"issn":["2050-5094"]},"oa":1,"status":"public","ec_funded":1,"month":"10","year":"2022","date_updated":"2023-08-04T09:00:35Z","abstract":[{"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.","lang":"eng"}],"_id":"12148","article_number":"e96","ddc":["510"],"scopus_import":"1","file_date_updated":"2023-01-24T10:02:40Z","citation":{"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>.","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.","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.","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)."},"intvolume":"        10","publication_status":"published","doi":"10.1017/fms.2022.86","date_published":"2022-10-27T00:00:00Z","oa_version":"Published Version"},{"scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.13719","open_access":"1"}],"intvolume":"        43","citation":{"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>.","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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","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.","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>"},"doi":"10.1137/21m1424408","publication_status":"published","date_published":"2022-07-01T00:00:00Z","oa_version":"Preprint","oa":1,"publication_identifier":{"eissn":["1095-7162"],"issn":["0895-4798"]},"status":"public","month":"07","year":"2022","abstract":[{"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].","lang":"eng"}],"issue":"3","arxiv":1,"date_updated":"2023-01-27T06:56:06Z","_id":"12179","article_type":"original","article_processing_charge":"No","keyword":["Analysis"],"quality_controlled":"1","volume":43,"external_id":{"arxiv":["2105.13719"]},"publication":"SIAM Journal on Matrix Analysis and Applications","date_created":"2023-01-12T12:12:38Z","page":"1469-1487","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"type":"journal_article","title":"On the condition number of the shifted real Ginibre ensemble","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Society for Industrial and Applied Mathematics","day":"01","author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}]},{"publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Density of small singular values of the shifted real Ginibre ensemble","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.","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"isi":1,"file":[{"content_type":"application/pdf","relation":"main_file","success":1,"file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","date_created":"2023-01-27T11:06:47Z","creator":"dernst","file_id":"12424","checksum":"5582f059feeb2f63e2eb68197a34d7dc","access_level":"open_access"}],"article_type":"original","article_processing_charge":"No","external_id":{"isi":["000796323500001"]},"volume":23,"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"quality_controlled":"1","has_accepted_license":"1","date_created":"2023-01-16T09:50:26Z","page":"3981-4002","publication":"Annales Henri Poincaré","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"status":"public","oa":1,"publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"month":"11","date_updated":"2023-08-04T09:33:52Z","issue":"11","abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"year":"2022","_id":"12232","file_date_updated":"2023-01-27T11:06:47Z","scopus_import":"1","ddc":["510"],"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <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>","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.","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>","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>.","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>."},"intvolume":"        23","publication_status":"published","doi":"10.1007/s00023-022-01188-8","oa_version":"Published Version","date_published":"2022-11-01T00:00:00Z"},{"type":"journal_article","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Journal of Mathematical Physics","date_created":"2023-01-16T09:52:58Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"quality_controlled":"1","volume":63,"external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"article_processing_charge":"Yes (via OA deal)","article_type":"original","isi":1,"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"file":[{"success":1,"file_size":7356807,"content_type":"application/pdf","relation":"main_file","date_created":"2023-01-30T08:01:10Z","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","date_updated":"2023-01-30T08:01:10Z","access_level":"open_access","checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436","creator":"dernst"}],"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.","day":"14","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"AIP Publishing","title":"Directional extremal statistics for Ginibre eigenvalues","oa_version":"Published Version","date_published":"2022-10-14T00:00:00Z","doi":"10.1063/5.0104290","publication_status":"published","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10. AIP Publishing, 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>","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","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>","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>."},"intvolume":"        63","file_date_updated":"2023-01-30T08:01:10Z","scopus_import":"1","ddc":["510","530"],"article_number":"103303","_id":"12243","arxiv":1,"abstract":[{"text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ","lang":"eng"}],"issue":"10","date_updated":"2023-08-04T09:40:02Z","year":"2022","month":"10","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]}},{"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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","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>"},"ddc":["510"],"file_date_updated":"2023-01-30T11:59:21Z","scopus_import":"1","date_published":"2022-09-12T00:00:00Z","oa_version":"Published Version","doi":"10.1214/22-ejp838","publication_status":"published","ec_funded":1,"month":"09","oa":1,"publication_identifier":{"eissn":["1083-6489"]},"status":"public","_id":"12290","year":"2022","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,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"quality_controlled":"1","external_id":{"isi":["000910863700003"]},"article_type":"original","article_processing_charge":"No","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Electronic Journal of Probability","page":"1-38","date_created":"2023-01-16T10:04:38Z","has_accepted_license":"1","title":"Optimal multi-resolvent local laws for Wigner matrices","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Mathematical Statistics","file":[{"file_name":"2022_ElecJournProbability_Cipolloni.pdf","date_updated":"2023-01-30T11:59:21Z","date_created":"2023-01-30T11:59:21Z","file_id":"12464","creator":"dernst","checksum":"bb647b48fbdb59361210e425c220cdcb","access_level":"open_access","relation":"main_file","content_type":"application/pdf","success":1,"file_size":502149}],"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"isi":1,"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"day":"12","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"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."},{"month":"02","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"_id":"8601","abstract":[{"text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.","lang":"eng"}],"arxiv":1,"date_updated":"2024-03-07T15:07:53Z","year":"2021","citation":{"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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","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>","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>.","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.","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)."},"file_date_updated":"2020-10-05T14:53:40Z","scopus_import":"1","ddc":["510"],"oa_version":"Published Version","date_published":"2021-02-01T00:00:00Z","doi":"10.1007/s00440-020-01003-7","publication_status":"published","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Edge universality for non-Hermitian random matrices","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"isi":1,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"file":[{"file_size":497032,"success":1,"relation":"main_file","content_type":"application/pdf","date_created":"2020-10-05T14:53:40Z","date_updated":"2020-10-05T14:53:40Z","file_name":"2020_ProbTheory_Cipolloni.pdf","access_level":"open_access","checksum":"611ae28d6055e1e298d53a57beb05ef4","creator":"dernst","file_id":"8612"}],"day":"01","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"article_processing_charge":"Yes (via OA deal)","article_type":"original","type":"journal_article","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Probability Theory and Related Fields","date_created":"2020-10-04T22:01:37Z"},{"_id":"9022","year":"2021","date_updated":"2023-09-07T13:29:32Z","abstract":[{"text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.","lang":"eng"}],"ec_funded":1,"month":"01","oa":1,"publication_identifier":{"issn":["2663-337X"]},"status":"public","date_published":"2021-01-25T00:00:00Z","oa_version":"Published Version","publication_status":"published","doi":"10.15479/AT:ISTA:9022","citation":{"ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","apa":"Cipolloni, G. (2021). <i>Fluctuations in the spectrum of random matrices</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>","mla":"Cipolloni, Giorgio. <i>Fluctuations in the Spectrum of Random Matrices</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021."},"ddc":["510"],"file_date_updated":"2021-01-25T14:19:10Z","file":[{"date_created":"2021-01-25T14:19:03Z","date_updated":"2021-01-25T14:19:03Z","file_name":"thesis.pdf","access_level":"open_access","creator":"gcipollo","file_id":"9043","checksum":"5a93658a5f19478372523ee232887e2b","file_size":4127796,"success":1,"relation":"main_file","content_type":"application/pdf"},{"file_name":"Thesis_files.zip","date_updated":"2021-01-25T14:19:10Z","date_created":"2021-01-25T14:19:10Z","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","creator":"gcipollo","file_id":"9044","access_level":"closed","content_type":"application/zip","relation":"source_file","file_size":12775206}],"project":[{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"},{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"}],"day":"25","acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","supervisor":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"alternative_title":["ISTA Thesis"],"degree_awarded":"PhD","title":"Fluctuations in the spectrum of random matrices","publisher":"Institute of Science and Technology Austria","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"type":"dissertation","date_created":"2021-01-21T18:16:54Z","page":"380","has_accepted_license":"1","article_processing_charge":"No"},{"external_id":{"isi":["000641855600001"],"arxiv":["2002.02438"]},"quality_controlled":"1","volume":26,"article_processing_charge":"No","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"has_accepted_license":"1","date_created":"2021-05-23T22:01:44Z","publication":"Electronic Journal of Probability","publisher":"Institute of Mathematical Statistics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Fluctuation around the circular law for random matrices with real entries","project":[{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"}],"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"isi":1,"file":[{"content_type":"application/pdf","relation":"main_file","file_size":865148,"success":1,"file_id":"9423","checksum":"864ab003ad4cffea783f65aa8c2ba69f","creator":"kschuh","access_level":"open_access","date_updated":"2021-05-25T13:24:19Z","file_name":"2021_EJP_Cipolloni.pdf","date_created":"2021-05-25T13:24:19Z"}],"day":"23","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        26","citation":{"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>.","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.","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","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.","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>"},"scopus_import":"1","file_date_updated":"2021-05-25T13:24:19Z","ddc":["510"],"oa_version":"Published Version","date_published":"2021-03-23T00:00:00Z","publication_status":"published","doi":"10.1214/21-EJP591","month":"03","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"eissn":["10836489"]},"article_number":"24","_id":"9412","date_updated":"2023-08-08T13:39:19Z","abstract":[{"lang":"eng","text":"We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness."}],"arxiv":1,"year":"2021"},{"page":"1005–1048","date_created":"2021-11-07T23:01:25Z","publication":"Communications in Mathematical Physics","has_accepted_license":"1","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","article_type":"original","external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"quality_controlled":"1","volume":388,"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"29","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","file":[{"file_size":841426,"success":1,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_id":"10715","creator":"cchlebak","date_created":"2022-02-02T10:19:55Z","date_updated":"2022-02-02T10:19:55Z","file_name":"2021_CommunMathPhys_Cipolloni.pdf"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"isi":1,"title":"Eigenstate thermalization hypothesis for Wigner matrices","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","doi":"10.1007/s00220-021-04239-z","date_published":"2021-10-29T00:00:00Z","oa_version":"Published Version","ddc":["510"],"scopus_import":"1","file_date_updated":"2022-02-02T10:19:55Z","citation":{"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>","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.","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>.","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>","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048."},"intvolume":"       388","year":"2021","date_updated":"2023-08-14T10:29:49Z","issue":"2","arxiv":1,"abstract":[{"text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).","lang":"eng"}],"_id":"10221","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"status":"public","month":"10"},{"day":"01","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"isi":1,"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"}],"publisher":"World Scientific Publishing","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","date_created":"2019-05-26T21:59:14Z","publication":"Random Matrices: Theory and Application","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"article_processing_charge":"No","article_type":"original","external_id":{"isi":["000547464400001"],"arxiv":["1806.08751"]},"volume":9,"quality_controlled":"1","date_updated":"2023-08-28T08:38:48Z","arxiv":1,"abstract":[{"lang":"eng","text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish."}],"issue":"3","year":"2020","article_number":"2050006","_id":"6488","status":"public","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"oa":1,"month":"07","ec_funded":1,"publication_status":"published","doi":"10.1142/S2010326320500069","oa_version":"Preprint","date_published":"2020-07-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"scopus_import":"1","citation":{"apa":"Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>.","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>. World Scientific Publishing, 2020. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>.","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. 2020;9(3). doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3. World Scientific Publishing, 2020.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020)."},"intvolume":"         9"},{"year":"2020","arxiv":1,"issue":"1","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)."}],"date_updated":"2024-03-04T10:33:15Z","_id":"15063","publication_identifier":{"issn":["2690-1005","2690-0998"]},"oa":1,"status":"public","ec_funded":1,"month":"11","doi":"10.2140/pmp.2020.1.101","publication_status":"published","date_published":"2020-11-16T00:00:00Z","oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"intvolume":"         1","citation":{"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>.","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>","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.","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>.","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.","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."},"day":"16","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","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder"}],"project":[{"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","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}],"title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Mathematical Sciences Publishers","publication":"Probability and Mathematical Physics","page":"101-146","date_created":"2024-03-04T10:27:57Z","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","article_processing_charge":"No","quality_controlled":"1","keyword":["General Medicine"],"volume":1,"external_id":{"arxiv":["1908.01653"]}}]