[{"date_published":"2026-01-01T00:00:00Z","oaworkid":1,"article_processing_charge":"Yes (via OA deal)","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"Elsevier","ddc":["510"],"year":"2026","article_number":"111180","_id":"20328","external_id":{"arxiv":["2411.16572"],"isi":["001583178200001"],"oaworkid":["w4413883397"]},"issue":"1","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan"}],"isi":1,"intvolume":"       290","volume":290,"corr_author":"1","month":"01","department":[{"_id":"LaEr"}],"publication_status":"published","day":"01","ec_funded":1,"doi":"10.1016/j.jfa.2025.111180","arxiv":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"quality_controlled":"1","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"ista":"Cipolloni G, Erdös L, Xu Y. 2026. Optimal decay of eigenvector overlap for non-Hermitian random matrices. Journal of Functional Analysis. 290(1), 111180.","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">https://doi.org/10.1016/j.jfa.2025.111180</a>.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Functional Analysis 290 (2026).","mla":"Cipolloni, Giorgio, et al. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 290, no. 1, 111180, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">10.1016/j.jfa.2025.111180</a>.","ama":"Cipolloni G, Erdös L, Xu Y. Optimal decay of eigenvector overlap for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2026;290(1). doi:<a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">10.1016/j.jfa.2025.111180</a>","apa":"Cipolloni, G., Erdös, L., &#38; Xu, Y. (2026). Optimal decay of eigenvector overlap for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">https://doi.org/10.1016/j.jfa.2025.111180</a>","ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Optimal decay of eigenvector overlap for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 290, no. 1. Elsevier, 2026."},"file":[{"file_name":"2026_JourFuncAnalysis_Cipolloni.pdf","file_id":"20947","date_created":"2026-01-05T13:05:47Z","creator":"dernst","file_size":2503887,"date_updated":"2026-01-05T13:05:47Z","access_level":"open_access","success":1,"checksum":"ee53d5e695f0df11e017c8c9242a2b04","relation":"main_file","content_type":"application/pdf"}],"scopus_import":"1","acknowledgement":"Partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Partially supported by National Key R&D Program of China No. 2024YFA1013503.","article_type":"original","OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Optimal decay of eigenvector overlap for non-Hermitian random matrices","OA_type":"hybrid","has_accepted_license":"1","oa":1,"abstract":[{"text":"We consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.","lang":"eng"}],"date_created":"2025-09-10T05:46:07Z","publication":"Journal of Functional Analysis","publication_identifier":{"issn":["0022-1236"]},"file_date_updated":"2026-01-05T13:05:47Z","PlanS_conform":"1","type":"journal_article","date_updated":"2026-06-03T13:12:14Z"},{"intvolume":"        53","volume":53,"_id":"21271","external_id":{"arxiv":["2404.17512"]},"issue":"6","author":[{"last_name":"Campbell","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","full_name":"Campbell, Andrew J","first_name":"Andrew J"},{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Ji","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang"}],"publisher":"Institute of Mathematical Statistics","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2025","date_published":"2025-11-01T00:00:00Z","article_processing_charge":"No","page":"2256-2308","abstract":[{"lang":"eng","text":"For general non-Hermitian large random matrices X and deterministic deformation matrices A, we prove that the local eigenvalue statistics of A+X close to the typical edge points of its spectrum are universal. Furthermore, we show that, under natural assumptions, on A the spectrum of A+X does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of Spec(A+X) is deterministic."}],"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"date_created":"2026-02-17T07:58:20Z","publication":"The Annals of Probability","date_updated":"2026-02-18T08:35:38Z","type":"journal_article","OA_place":"repository","article_type":"original","OA_type":"green","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the spectral edge of non-Hermitian random matrices","oa":1,"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2404.17512"}],"citation":{"ista":"Campbell AJ, Cipolloni G, Erdös L, Ji HC. 2025. On the spectral edge of non-Hermitian random matrices. The Annals of Probability. 53(6), 2256–2308.","chicago":"Campbell, Andrew J, Giorgio Cipolloni, László Erdös, and Hong Chang Ji. “On the Spectral Edge of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-aop1761\">https://doi.org/10.1214/25-aop1761</a>.","mla":"Campbell, Andrew J., et al. “On the Spectral Edge of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 53, no. 6, Institute of Mathematical Statistics, 2025, pp. 2256–308, doi:<a href=\"https://doi.org/10.1214/25-aop1761\">10.1214/25-aop1761</a>.","short":"A.J. Campbell, G. Cipolloni, L. Erdös, H.C. Ji, The Annals of Probability 53 (2025) 2256–2308.","apa":"Campbell, A. J., Cipolloni, G., Erdös, L., &#38; Ji, H. C. (2025). On the spectral edge of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aop1761\">https://doi.org/10.1214/25-aop1761</a>","ama":"Campbell AJ, Cipolloni G, Erdös L, Ji HC. On the spectral edge of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2025;53(6):2256-2308. doi:<a href=\"https://doi.org/10.1214/25-aop1761\">10.1214/25-aop1761</a>","ieee":"A. J. Campbell, G. Cipolloni, L. Erdös, and H. C. Ji, “On the spectral edge of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 53, no. 6. Institute of Mathematical Statistics, pp. 2256–2308, 2025."},"acknowledgement":"The authors would like to thank the anonymous referee for providing helpful comments and suggestions. We also thank Joscha Henheik and Volodymyr Riabov for pointing out a gap in an earlier version of the proof of equation (3.18). The first, third, and fourth authors are supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","month":"11","day":"01","doi":"10.1214/25-aop1761","ec_funded":1,"department":[{"_id":"LaEr"}],"publication_status":"published","arxiv":1,"oa_version":"Preprint","quality_controlled":"1","language":[{"iso":"eng"}]},{"external_id":{"arxiv":["2410.10718"]},"_id":"19546","author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Oleksii","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"year":"2025","date_published":"2025-01-30T00:00:00Z","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We study the sensitivity of the eigenvectors of random matrices, showing that\r\neven small perturbations make the eigenvectors almost orthogonal. More\r\nprecisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show\r\nthat their bulk eigenvectors become asymptotically orthogonal as soon as\r\n$\\mathrm{Tr}(D_1-D_2)^2\\gg 1$, or their respective energies are separated on a\r\nscale much bigger than the local eigenvalue spacing. Furthermore, we show that\r\nquadratic forms of eigenvectors of $W+D_1$, $W+D_2$ with any deterministic\r\nmatrix $A\\in\\mathbf{C}^{N\\times N}$ in a specific subspace of codimension one\r\nare of size $N^{-1/2}$. This proves a generalization of the Eigenstate\r\nThermalization Hypothesis to eigenvectors belonging to two different spectral\r\nfamilies."}],"date_created":"2025-04-11T08:34:49Z","publication":"arXiv","date_updated":"2026-04-07T12:37:11Z","type":"preprint","OA_place":"repository","title":"Eigenvector decorrelation for random matrices","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.10718"}],"status":"public","citation":{"ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>arXiv</i>. .","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (n.d.). Eigenvector decorrelation for random matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.10718\">https://doi.org/10.48550/arXiv.2410.10718</a>","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10718\">10.48550/arXiv.2410.10718</a>","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.10718\">https://doi.org/10.48550/arXiv.2410.10718</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","mla":"Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10718\">10.48550/arXiv.2410.10718</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.10718\">10.48550/arXiv.2410.10718</a>."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","month":"01","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"day":"30","ec_funded":1,"doi":"10.48550/arXiv.2410.10718","publication_status":"draft","department":[{"_id":"LaEr"}],"arxiv":1,"language":[{"iso":"eng"}],"oa_version":"Preprint"},{"author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang"}],"isi":1,"_id":"19737","external_id":{"isi":["001493091900001"]},"article_processing_charge":"Yes (via OA deal)","date_published":"2025-01-01T00:00:00Z","year":"2025","article_number":"050603","ddc":["500"],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publisher":"Springer Nature","oa":1,"title":"Non–Hermitian spectral universality at critical points","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"hybrid","article_type":"original","OA_place":"publisher","type":"journal_article","date_updated":"2026-06-18T18:17:57Z","date_created":"2025-05-25T22:16:59Z","publication":"Probability Theory and Related Fields","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"abstract":[{"lang":"eng","text":"For general large non–Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A + X close to the critical edge points of its spectrum are universal. This concludes the proof of the third and last remaining typical universality class for non–Hermitian random matrices (for normal deformations), after bulk and sharp edge universalities have been established in recent years."}],"language":[{"iso":"eng"}],"oa_version":"Published Version","quality_controlled":"1","publication_status":"epub_ahead","department":[{"_id":"LaEr"}],"doi":"10.1007/s00440-025-01384-7","day":"01","ec_funded":1,"month":"01","corr_author":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","scopus_import":"1","citation":{"ieee":"G. Cipolloni, L. Erdös, and H. C. Ji, “Non–Hermitian spectral universality at critical points,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025.","ama":"Cipolloni G, Erdös L, Ji HC. Non–Hermitian spectral universality at critical points. <i>Probability Theory and Related Fields</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s00440-025-01384-7\">10.1007/s00440-025-01384-7</a>","apa":"Cipolloni, G., Erdös, L., &#38; Ji, H. C. (2025). Non–Hermitian spectral universality at critical points. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01384-7\">https://doi.org/10.1007/s00440-025-01384-7</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Hong Chang Ji. “Non–Hermitian Spectral Universality at Critical Points.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01384-7\">https://doi.org/10.1007/s00440-025-01384-7</a>.","mla":"Cipolloni, Giorgio, et al. “Non–Hermitian Spectral Universality at Critical Points.” <i>Probability Theory and Related Fields</i>, 050603, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00440-025-01384-7\">10.1007/s00440-025-01384-7</a>.","short":"G. Cipolloni, L. Erdös, H.C. Ji, Probability Theory and Related Fields (2025).","ista":"Cipolloni G, Erdös L, Ji HC. 2025. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields., 050603."},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-025-01384-7"}]},{"status":"public","main_file_link":[{"url":"https://doi.org/10.1007/s00440-025-01422-4","open_access":"1"}],"citation":{"mla":"Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00440-025-01422-4\">10.1007/s00440-025-01422-4</a>.","short":"Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025).","chicago":"Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01422-4\">https://doi.org/10.1007/s00440-025-01422-4</a>.","ista":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields.","ieee":"Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation transition in the Wigner minor process,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025.","ama":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s00440-025-01422-4\">10.1007/s00440-025-01422-4</a>","apa":"Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025). Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01422-4\">https://doi.org/10.1007/s00440-025-01422-4</a>"},"scopus_import":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121 and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","month":"09","doi":"10.1007/s00440-025-01422-4","ec_funded":1,"day":"20","publication_status":"epub_ahead","department":[{"_id":"LaEr"}],"arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider the Wigner minor process, i.e. the eigenvalues of an N\\times N Wigner matrix H^{(N)} together with the eigenvalues of all its n\\times n minors, H^{(n)}, n\\le N. The top eigenvalues of H^{(N)} and those of its immediate minor H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical transition regime around k\\sim N^{2/3} was analyzed by Forrester and Nagao (J. Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality."}],"publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"publication":"Probability Theory and Related Fields","date_created":"2025-10-16T13:10:26Z","PlanS_conform":"1","date_updated":"2026-06-18T18:23:40Z","type":"journal_article","OA_place":"publisher","article_type":"original","OA_type":"hybrid","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Decorrelation transition in the Wigner minor process","oa":1,"publisher":"Springer Nature","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"ddc":["500"],"year":"2025","date_published":"2025-09-20T00:00:00Z","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001574640900001"],"arxiv":["2503.06549"]},"_id":"20478","author":[{"first_name":"Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"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","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev","first_name":"Oleksii","orcid":"0000-0003-1491-4623"}],"isi":1},{"volume":188,"intvolume":"       188","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"isi":1,"_id":"14408","external_id":{"arxiv":["2210.12060"],"isi":["001118972500001"]},"year":"2024","publisher":"Springer Nature","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"article_processing_charge":"No","page":"1131-1182","date_published":"2024-04-01T00:00:00Z","date_updated":"2025-08-05T13:28:15Z","type":"journal_article","abstract":[{"text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator.","lang":"eng"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"publication":"Probability Theory and Related Fields","date_created":"2023-10-08T22:01:17Z","oa":1,"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Mesoscopic central limit theorem for non-Hermitian random matrices","scopus_import":"1","acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.\r\nLászló Erdős supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Dominik Schröder supported by the SNSF Ambizione Grant PZ00P2 209089.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.12060"}],"status":"public","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182.","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, 2024. <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>, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2024. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 188, 1131–1182.","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>, vol. 188. Springer Nature, pp. 1131–1182, 2024.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2024;188:1131-1182. doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>"},"arxiv":1,"language":[{"iso":"eng"}],"oa_version":"Preprint","quality_controlled":"1","month":"04","day":"01","doi":"10.1007/s00440-023-01229-1","ec_funded":1,"department":[{"_id":"LaEr"}],"publication_status":"published"},{"abstract":[{"lang":"eng","text":"We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between."}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"date_created":"2024-05-26T22:00:57Z","publication":"Journal of Functional Analysis","file_date_updated":"2025-06-24T13:14:21Z","date_updated":"2026-04-07T12:37:11Z","type":"journal_article","OA_place":"publisher","article_type":"original","OA_type":"hybrid","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","has_accepted_license":"1","oa":1,"status":"public","file":[{"date_updated":"2025-06-24T13:14:21Z","creator":"dernst","file_size":1374854,"file_id":"19891","date_created":"2025-06-24T13:14:21Z","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","content_type":"application/pdf","checksum":"07d3f73e0c56e68eb110851842c22ee0","relation":"main_file","access_level":"open_access","success":1}],"citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 287(4), 110495.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024).","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 287, no. 4, 110495, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>.","ama":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2024;287(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 287, no. 4. Elsevier, 2024."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"scopus_import":"1","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","corr_author":"1","month":"08","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"ec_funded":1,"day":"15","doi":"10.1016/j.jfa.2024.110495","department":[{"_id":"LaEr"}],"publication_status":"published","oa_version":"Published Version","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"       287","volume":287,"external_id":{"isi":["001325502400001"]},"_id":"17049","issue":"4","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","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"isi":1,"publisher":"Elsevier","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"ddc":["510"],"article_number":"110495","year":"2024","date_published":"2024-08-15T00:00:00Z","article_processing_charge":"Yes (via OA deal)"},{"author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"}],"_id":"18656","issue":"6","external_id":{"arxiv":["2402.17609"]},"volume":28,"intvolume":"        28","page":"2025-2083","article_processing_charge":"No","date_published":"2024-10-30T00:00:00Z","year":"2024","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"International Press","oa":1,"title":"Out-of-time-ordered correlators for Wigner matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"green","article_type":"original","OA_place":"repository","type":"journal_article","date_updated":"2026-04-07T12:37:10Z","date_created":"2024-12-15T23:01:51Z","publication":"Advances in Theoretical and Mathematical Physics","publication_identifier":{"issn":["1095-0761"],"eissn":["1095-0753"]},"abstract":[{"text":"We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables \r\n and \r\n in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11]).","lang":"eng"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"quality_controlled":"1","arxiv":1,"publication_status":"published","department":[{"_id":"LaEr"}],"ec_funded":1,"day":"30","doi":"10.4310/ATMP.241031013250","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"corr_author":"1","month":"10","scopus_import":"1","acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2024. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>.","mla":"Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6, International Press, 2024, pp. 2025–83, doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>","ama":"Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2024;28(6):2025-2083. doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6. International Press, pp. 2025–2083, 2024."},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.17609"}]},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","ama":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. ."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.05488"}],"status":"public","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","publication_status":"draft","department":[{"_id":"LaEr"}],"ec_funded":1,"doi":"10.48550/arXiv.2309.05488","day":"17","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"month":"12","corr_author":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","arxiv":1,"publication":"arXiv","date_created":"2025-04-11T08:19:22Z","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling."}],"type":"preprint","date_updated":"2026-04-07T12:37:11Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"Eigenstate thermalisation at the edge for Wigner matrices","OA_place":"repository","oa":1,"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2024","date_published":"2024-12-17T00:00:00Z","article_processing_charge":"No","_id":"19545","external_id":{"arxiv":["2309.05488"]},"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","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"}]},{"corr_author":"1","month":"06","department":[{"_id":"LaEr"}],"publication_status":"published","day":"01","ec_funded":1,"doi":"10.1063/5.0209705","arxiv":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"quality_controlled":"1","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.15643"}],"citation":{"ista":"Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.","mla":"Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2024. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>.","ama":"Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. 2024;65(6). doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>","apa":"Cipolloni, G., Erdös, L., &#38; Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>","ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6. AIP Publishing, 2024."},"scopus_import":"1","acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","article_type":"original","title":"Precise asymptotics for the spectral radius of a large random matrix","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"abstract":[{"lang":"eng","text":"We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion."}],"publication":"Journal of Mathematical Physics","date_created":"2024-08-04T22:01:22Z","publication_identifier":{"issn":["0022-2488"]},"type":"journal_article","date_updated":"2025-09-08T08:44:57Z","date_published":"2024-06-01T00:00:00Z","article_processing_charge":"No","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"publisher":"AIP Publishing","year":"2024","article_number":"063302","issue":"6","_id":"17375","external_id":{"isi":["001252240700002"],"arxiv":["2210.15643"]},"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205"}],"isi":1,"intvolume":"        65","volume":65},{"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"isi":1,"_id":"11741","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"volume":185,"intvolume":"       185","page":"1183–1218","article_processing_charge":"Yes (via OA deal)","date_published":"2023-04-01T00:00:00Z","year":"2023","ddc":["510"],"publisher":"Springer Nature","oa":1,"has_accepted_license":"1","title":"Quenched universality for deformed Wigner matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","type":"journal_article","date_updated":"2024-10-09T21:03:02Z","file_date_updated":"2023-08-14T12:47:32Z","date_created":"2022-08-07T22:02:00Z","publication":"Probability Theory and Related Fields","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"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."}],"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","arxiv":1,"department":[{"_id":"LaEr"}],"publication_status":"published","day":"01","doi":"10.1007/s00440-022-01156-7","corr_author":"1","month":"04","scopus_import":"1","acknowledgement":"The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","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>.","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.","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.","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>","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>"},"file":[{"date_updated":"2023-08-14T12:47:32Z","file_size":782278,"creator":"dernst","date_created":"2023-08-14T12:47:32Z","file_id":"14054","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","content_type":"application/pdf","relation":"main_file","checksum":"b9247827dae5544d1d19c37abe547abc","success":1,"access_level":"open_access"}],"status":"public"},{"year":"2023","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"Institute of Mathematical Statistics","article_processing_charge":"No","page":"447-489","date_published":"2023-02-01T00:00:00Z","volume":33,"intvolume":"        33","isi":1,"author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"issue":"1","_id":"12761","external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"scopus_import":"1","acknowledgement":"The second author is partially funded by the ERC Advanced Grant “RMTBEYOND” No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"status":"public","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.","mla":"Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","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>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. 2023;33(1):447-489. doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>","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."},"arxiv":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"quality_controlled":"1","corr_author":"1","month":"02","department":[{"_id":"LaEr"}],"publication_status":"published","ec_funded":1,"day":"01","doi":"10.1214/22-AAP1820","type":"journal_article","date_updated":"2025-04-14T07:57:19Z","abstract":[{"lang":"eng","text":"We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"date_created":"2023-03-26T22:01:08Z","publication":"Annals of Applied Probability","publication_identifier":{"issn":["1050-5164"]},"oa":1,"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Functional central limit theorems for Wigner matrices"},{"status":"public","file":[{"date_updated":"2023-10-04T12:09:18Z","file_size":859967,"creator":"dernst","date_created":"2023-10-04T12:09:18Z","file_id":"14397","file_name":"2023_CommMathPhysics_Cipolloni.pdf","content_type":"application/pdf","relation":"main_file","checksum":"72057940f76654050ca84a221f21786c","success":1,"access_level":"open_access"}],"citation":{"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>","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","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>."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"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.","scopus_import":"1","corr_author":"1","month":"07","doi":"10.1007/s00220-023-04692-y","day":"01","ec_funded":1,"publication_status":"published","department":[{"_id":"LaEr"}],"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics."}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication":"Communications in Mathematical Physics","date_created":"2023-04-02T22:01:11Z","file_date_updated":"2023-10-04T12:09:18Z","date_updated":"2025-04-14T07:57:19Z","type":"journal_article","article_type":"original","title":"On the spectral form factor for random matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","oa":1,"publisher":"Springer Nature","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"ddc":["510"],"year":"2023","date_published":"2023-07-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","page":"1665-1700","intvolume":"       401","volume":401,"external_id":{"isi":["000957343500001"]},"_id":"12792","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"isi":1},{"intvolume":"        11","volume":11,"_id":"14343","external_id":{"arxiv":["2301.05181"],"isi":["001051980200001"]},"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","full_name":"Erdös, László","last_name":"Erdös"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"first_name":"Oleksii","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii"}],"isi":1,"publisher":"Cambridge University Press","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"ddc":["510"],"article_number":"e74","year":"2023","date_published":"2023-08-23T00:00:00Z","article_processing_charge":"Yes","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."}],"publication_identifier":{"eissn":["2050-5094"]},"publication":"Forum of Mathematics, Sigma","date_created":"2023-09-17T22:01:09Z","file_date_updated":"2023-09-20T11:09:35Z","date_updated":"2026-04-07T12:37:10Z","type":"journal_article","article_type":"original","title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","oa":1,"status":"public","citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <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>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","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>.","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>","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>","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."},"file":[{"file_id":"14352","date_created":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","date_updated":"2023-09-20T11:09:35Z","creator":"dernst","file_size":852652,"access_level":"open_access","success":1,"content_type":"application/pdf","checksum":"eb747420e6a88a7796fa934151957676","relation":"main_file"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"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.","scopus_import":"1","corr_author":"1","month":"08","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"day":"23","ec_funded":1,"doi":"10.1017/fms.2023.70","publication_status":"published","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"arxiv":1,"oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}]},{"month":"11","corr_author":"1","department":[{"_id":"LaEr"}],"publication_status":"published","doi":"10.1214/23-aop1643","ec_funded":1,"day":"01","arxiv":1,"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"citation":{"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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","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>.","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>","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>","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."},"scopus_import":"1","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.","article_type":"original","title":"On the rightmost eigenvalue of non-Hermitian random matrices","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"oa":1,"abstract":[{"lang":"eng","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."}],"date_created":"2024-01-22T08:08:41Z","publication":"The Annals of Probability","publication_identifier":{"issn":["0091-1798"]},"type":"journal_article","date_updated":"2025-09-09T14:23:34Z","date_published":"2023-11-01T00:00:00Z","article_processing_charge":"No","page":"2192-2242","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"publisher":"Institute of Mathematical Statistics","year":"2023","_id":"14849","external_id":{"isi":["001112165000004"],"arxiv":["2206.04448"]},"issue":"6","author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder"},{"first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"isi":1,"intvolume":"        51","volume":51},{"citation":{"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.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","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>.","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>.","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."},"file":[{"access_level":"open_access","success":1,"content_type":"application/pdf","checksum":"8346bc2642afb4ccb7f38979f41df5d9","relation":"main_file","date_created":"2023-10-04T09:21:48Z","file_id":"14388","file_name":"2023_CommPureMathematics_Cipolloni.pdf","date_updated":"2023-10-04T09:21:48Z","creator":"dernst","file_size":803440}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"status":"public","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.","scopus_import":"1","ec_funded":1,"day":"01","doi":"10.1002/cpa.22028","department":[{"_id":"LaEr"}],"publication_status":"published","month":"05","corr_author":"1","quality_controlled":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"arxiv":1,"publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"date_created":"2021-12-05T23:01:41Z","publication":"Communications on Pure and Applied Mathematics","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"}],"date_updated":"2025-03-31T16:00:54Z","type":"journal_article","file_date_updated":"2023-10-04T09:21:48Z","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","has_accepted_license":"1","oa":1,"ddc":["510"],"publisher":"Wiley","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"year":"2023","date_published":"2023-05-01T00:00:00Z","page":"946-1034","article_processing_charge":"Yes (via OA deal)","intvolume":"        76","volume":76,"_id":"10405","external_id":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"issue":"5","isi":1,"author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}]},{"scopus_import":"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.","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","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>","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>"},"status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2103.06730","open_access":"1"}],"quality_controlled":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","arxiv":1,"publication_status":"published","department":[{"_id":"LaEr"}],"doi":"10.1214/21-AOP1552","day":"01","month":"05","type":"journal_article","date_updated":"2023-08-03T07:16:53Z","date_created":"2022-05-29T22:01:53Z","publication":"Annals of Probability","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"abstract":[{"text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","article_type":"original","year":"2022","publisher":"Institute of Mathematical Statistics","page":"984-1012","article_processing_charge":"No","date_published":"2022-05-01T00:00:00Z","volume":50,"intvolume":"        50","isi":1,"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"_id":"11418","external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"issue":"3"},{"date_created":"2023-01-12T12:07:30Z","publication":"Forum of Mathematics, Sigma","publication_identifier":{"issn":["2050-5094"]},"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"}],"type":"journal_article","date_updated":"2025-04-14T07:57:18Z","file_date_updated":"2023-01-24T10:02:40Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Rank-uniform local law for Wigner matrices","article_type":"original","oa":1,"has_accepted_license":"1","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"citation":{"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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","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.","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>","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>"},"file":[{"success":1,"access_level":"open_access","relation":"main_file","checksum":"94a049aeb1eea5497aa097712a73c400","content_type":"application/pdf","file_name":"2022_ForumMath_Cipolloni.pdf","date_created":"2023-01-24T10:02:40Z","file_id":"12356","file_size":817089,"creator":"dernst","date_updated":"2023-01-24T10:02:40Z"}],"status":"public","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.","scopus_import":"1","publication_status":"published","department":[{"_id":"LaEr"}],"doi":"10.1017/fms.2022.86","ec_funded":1,"day":"27","corr_author":"1","month":"10","oa_version":"Published Version","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"        10","volume":10,"external_id":{"isi":["000873719200001"]},"_id":"12148","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"isi":1,"ddc":["510"],"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"Cambridge University Press","year":"2022","article_number":"e96","date_published":"2022-10-27T00:00:00Z","article_processing_charge":"No"},{"date_created":"2023-01-12T12:12:38Z","publication":"SIAM Journal on Matrix Analysis and Applications","publication_identifier":{"issn":["0895-4798"],"eissn":["1095-7162"]},"abstract":[{"lang":"eng","text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146]."}],"type":"journal_article","date_updated":"2025-09-10T09:51:27Z","title":"On the condition number of the shifted real Ginibre ensemble","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","oa":1,"keyword":["Analysis"],"citation":{"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.","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>","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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","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."},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"scopus_import":"1","publication_status":"published","department":[{"_id":"LaEr"}],"doi":"10.1137/21m1424408","day":"01","month":"07","corr_author":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","quality_controlled":"1","arxiv":1,"intvolume":"        43","volume":43,"issue":"3","_id":"12179","external_id":{"isi":["001125796400002"],"arxiv":["2105.13719"]},"isi":1,"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"publisher":"Society for Industrial and Applied Mathematics","year":"2022","date_published":"2022-07-01T00:00:00Z","page":"1469-1487","article_processing_charge":"No"},{"language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","department":[{"_id":"LaEr"}],"publication_status":"published","day":"01","doi":"10.1007/s00023-022-01188-8","month":"11","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.","scopus_import":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"access_level":"open_access","success":1,"checksum":"5582f059feeb2f63e2eb68197a34d7dc","relation":"main_file","content_type":"application/pdf","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","file_id":"12424","date_created":"2023-01-27T11:06:47Z","creator":"dernst","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z"}],"citation":{"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.","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>","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>","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>.","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","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."},"status":"public","has_accepted_license":"1","oa":1,"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"title":"Density of small singular values of the shifted real Ginibre ensemble","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","type":"journal_article","date_updated":"2023-08-04T09:33:52Z","file_date_updated":"2023-01-27T11:06:47Z","date_created":"2023-01-16T09:50:26Z","publication":"Annales Henri Poincaré","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"abstract":[{"lang":"eng","text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold."}],"page":"3981-4002","article_processing_charge":"No","date_published":"2022-11-01T00:00:00Z","year":"2022","ddc":["510"],"publisher":"Springer Nature","isi":1,"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"issue":"11","_id":"12232","external_id":{"isi":["000796323500001"]},"volume":23,"intvolume":"        23"}]