[{"isi":1,"day":"01","PlanS_conform":"1","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_type":"original","doi":"10.1016/j.jfa.2025.111180","department":[{"_id":"LaEr"}],"file":[{"content_type":"application/pdf","checksum":"ee53d5e695f0df11e017c8c9242a2b04","success":1,"access_level":"open_access","date_updated":"2026-01-05T13:05:47Z","file_name":"2026_JourFuncAnalysis_Cipolloni.pdf","file_id":"20947","relation":"main_file","creator":"dernst","date_created":"2026-01-05T13:05:47Z","file_size":2503887}],"publication_status":"published","date_created":"2025-09-10T05:46:07Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","oaworkid":1,"issue":"1","_id":"20328","quality_controlled":"1","citation":{"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.","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>.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Functional Analysis 290 (2026).","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>.","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.","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>"},"date_updated":"2026-06-03T13:12:14Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"lang":"eng","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."}],"file_date_updated":"2026-01-05T13:05:47Z","oa":1,"language":[{"iso":"eng"}],"OA_type":"hybrid","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","title":"Optimal decay of eigenvector overlap for non-Hermitian random matrices","year":"2026","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":290,"date_published":"2026-01-01T00:00:00Z","oa_version":"Published Version","ddc":["510"],"article_number":"111180","external_id":{"arxiv":["2411.16572"],"isi":["001583178200001"],"oaworkid":["w4413883397"]},"acknowledgement":"Partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Partially supported by National Key R&D Program of China No. 2024YFA1013503.","author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","orcid":"0000-0003-1559-1205"}],"month":"01","intvolume":"       290","publication_identifier":{"issn":["0022-1236"]},"publisher":"Elsevier","publication":"Journal of Functional Analysis","OA_place":"publisher","has_accepted_license":"1","status":"public","arxiv":1,"corr_author":"1"},{"day":"26","PlanS_conform":"1","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_type":"original","department":[{"_id":"LaEr"}],"doi":"10.1007/s11005-025-02037-5","publication_status":"epub_ahead","date_created":"2026-01-04T23:01:33Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","_id":"20925","date_updated":"2026-01-05T11:22:25Z","quality_controlled":"1","citation":{"ista":"Erdös L, Henheik SJ, Vogel C. 2025. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 116, 5.","apa":"Erdös, L., Henheik, S. J., &#38; Vogel, C. (2025). Normal typicality and dynamical typicality for a random block-band matrix model. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-025-02037-5\">https://doi.org/10.1007/s11005-025-02037-5</a>","ama":"Erdös L, Henheik SJ, Vogel C. Normal typicality and dynamical typicality for a random block-band matrix model. <i>Letters in Mathematical Physics</i>. 2025;116. doi:<a href=\"https://doi.org/10.1007/s11005-025-02037-5\">10.1007/s11005-025-02037-5</a>","mla":"Erdös, László, et al. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” <i>Letters in Mathematical Physics</i>, vol. 116, 5, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s11005-025-02037-5\">10.1007/s11005-025-02037-5</a>.","ieee":"L. Erdös, S. J. Henheik, and C. Vogel, “Normal typicality and dynamical typicality for a random block-band matrix model,” <i>Letters in Mathematical Physics</i>, vol. 116. Springer Nature, 2025.","chicago":"Erdös, László, Sven Joscha Henheik, and Cornelia Vogel. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11005-025-02037-5\">https://doi.org/10.1007/s11005-025-02037-5</a>.","short":"L. Erdös, S.J. Henheik, C. Vogel, Letters in Mathematical Physics 116 (2025)."},"ec_funded":1,"abstract":[{"lang":"eng","text":"We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices (Erdős and Riabov in Commun Math Phys 405(12): 282, 2024) and an intricate analysis of the deterministic approximation."}],"language":[{"iso":"eng"}],"oa":1,"OA_type":"hybrid","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","title":"Normal typicality and dynamical typicality for a random block-band matrix model","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":116,"date_published":"2025-12-26T00:00:00Z","oa_version":"Published Version","pmid":1,"article_number":"5","ddc":["510"],"external_id":{"pmid":["41459414"]},"acknowledgement":"L.E. and J.H. are supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. Moreover, J.H. acknowledges (partial) financial support by the ERC Consolidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education, Research and Innovation). C.V. was (partially) supported by the German Academic Scholarship Foundation and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – TRR 352 – Project-ID 470903074. Moreover, C.V. acknowledges (partial) financial support by the ERC Starting Grant “FermiMath\" No. 101040991 and the ERC Consolidator Grant “RAMBAS” No. 10104424, funded by the European Union. Open access funding provided by Institute of Science and Technology (IST Austria).","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik"},{"id":"1cd0554a-ea28-11f0-9f40-ff76440883cd","last_name":"Vogel","first_name":"Cornelia","full_name":"Vogel, Cornelia"}],"month":"12","intvolume":"       116","main_file_link":[{"url":"https://doi.org/10.1007/s11005-025-02037-5","open_access":"1"}],"publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"publisher":"Springer Nature","publication":"Letters in Mathematical Physics","OA_place":"publisher","has_accepted_license":"1","status":"public","corr_author":"1"},{"arxiv":1,"corr_author":"1","status":"public","publication":"The Annals of Probability","OA_place":"repository","publisher":"Institute of Mathematical Statistics","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2404.17512","open_access":"1"}],"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"intvolume":"        53","month":"11","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.","author":[{"first_name":"Andrew J","full_name":"Campbell, Andrew J","last_name":"Campbell","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Ji, Hong Chang","first_name":"Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"external_id":{"arxiv":["2404.17512"]},"date_published":"2025-11-01T00:00:00Z","volume":53,"oa_version":"Preprint","year":"2025","page":"2256-2308","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the spectral edge of non-Hermitian random matrices","article_processing_charge":"No","OA_type":"green","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"date_updated":"2026-02-18T08:35:38Z","citation":{"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>","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>","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.","short":"A.J. Campbell, G. Cipolloni, L. Erdös, H.C. Ji, The Annals of Probability 53 (2025) 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>.","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.","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>."},"quality_controlled":"1","_id":"21271","issue":"6","date_created":"2026-02-17T07:58:20Z","publication_status":"published","type":"journal_article","doi":"10.1214/25-aop1761","department":[{"_id":"LaEr"}],"article_type":"original","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"day":"01"},{"page":"1991-2033","year":"2025","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","date_published":"2025-06-01T00:00:00Z","volume":26,"article_processing_charge":"Yes (via OA deal)","title":"Prethermalization for deformed Wigner matrices","acknowledgement":"All authors were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nJ.R. was additionally supported by the ERC Advanced Grant “LDRaM” No. 884584.\r\nWe thank Peter Reimann and Lennart Dabelow for helpful comments. Open access funding provided by Institute of Science and Technology (IST Austria).","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","full_name":"Reker, Jana","first_name":"Jana"},{"last_name":"Riabov","full_name":"Riabov, Volodymyr","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"ddc":["510"],"external_id":{"arxiv":["2310.06677"],"isi":["001385326500001"]},"publication_identifier":{"issn":["1424-0637"]},"month":"06","intvolume":"        26","has_accepted_license":"1","status":"public","corr_author":"1","arxiv":1,"publisher":"Springer Nature","publication":"Annales Henri Poincare","OA_place":"publisher","article_type":"original","isi":1,"day":"01","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"publication_status":"published","date_created":"2025-01-05T23:01:59Z","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"department":[{"_id":"LaEr"}],"doi":"10.1007/s00023-024-01518-y","file":[{"file_size":977773,"date_created":"2025-06-25T05:38:34Z","creator":"dernst","relation":"main_file","file_id":"19895","file_name":"2025_AnnalesHenriPoincare_Erdoes.pdf","date_updated":"2025-06-25T05:38:34Z","access_level":"open_access","success":1,"checksum":"49e6a934db540206f7eaa0c798553ded","content_type":"application/pdf"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17174"},{"relation":"dissertation_contains","id":"20575","status":"public"},{"id":"19540","relation":"dissertation_contains","status":"public"}]},"quality_controlled":"1","citation":{"mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” <i>Annales Henri Poincare</i>, vol. 26, Springer Nature, 2025, pp. 1991–2033, doi:<a href=\"https://doi.org/10.1007/s00023-024-01518-y\">10.1007/s00023-024-01518-y</a>.","ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner matrices,” <i>Annales Henri Poincare</i>, vol. 26. Springer Nature, pp. 1991–2033, 2025.","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” <i>Annales Henri Poincare</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00023-024-01518-y\">https://doi.org/10.1007/s00023-024-01518-y</a>.","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025) 1991–2033.","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. 2025. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 26, 1991–2033.","apa":"Erdös, L., Henheik, S. J., Reker, J., &#38; Riabov, V. (2025). Prethermalization for deformed Wigner matrices. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-024-01518-y\">https://doi.org/10.1007/s00023-024-01518-y</a>","ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner matrices. <i>Annales Henri Poincare</i>. 2025;26:1991-2033. doi:<a href=\"https://doi.org/10.1007/s00023-024-01518-y\">10.1007/s00023-024-01518-y</a>"},"date_updated":"2026-04-07T12:37:11Z","_id":"18764","OA_type":"hybrid","scopus_import":"1","ec_funded":1,"abstract":[{"text":"We prove that a class of weakly perturbed Hamiltonians of the form H_λ= H_0 + λW, with W being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by H_λ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order λ^{-2}. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix H_λ.","lang":"eng"}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-06-25T05:38:34Z"},{"article_type":"original","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"day":"30","isi":1,"type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2025-02-05T06:48:29Z","file":[{"file_id":"19004","relation":"main_file","date_created":"2025-02-05T07:01:40Z","file_size":828335,"creator":"dernst","content_type":"application/pdf","date_updated":"2025-02-05T07:01:40Z","file_name":"2025_LettersMathPhysics_Erdoes.pdf","checksum":"ee07edf5f85a6f2651926b2f8760af74","access_level":"open_access","success":1}],"department":[{"_id":"LaEr"}],"doi":"10.1007/s11005-025-01904-5","date_updated":"2026-04-07T12:37:10Z","citation":{"ista":"Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 115, 14.","ama":"Erdös L, Henheik SJ, Kolupaiev O. Loschmidt echo for deformed Wigner matrices. <i>Letters in Mathematical Physics</i>. 2025;115. doi:<a href=\"https://doi.org/10.1007/s11005-025-01904-5\">10.1007/s11005-025-01904-5</a>","apa":"Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025). Loschmidt echo for deformed Wigner matrices. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-025-01904-5\">https://doi.org/10.1007/s11005-025-01904-5</a>","ieee":"L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner matrices,” <i>Letters in Mathematical Physics</i>, vol. 115. Springer Nature, 2025.","mla":"Erdös, László, et al. “Loschmidt Echo for Deformed Wigner Matrices.” <i>Letters in Mathematical Physics</i>, vol. 115, 14, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s11005-025-01904-5\">10.1007/s11005-025-01904-5</a>.","short":"L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115 (2025).","chicago":"Erdös, László, Sven Joscha Henheik, and Oleksii Kolupaiev. “Loschmidt Echo for Deformed Wigner Matrices.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11005-025-01904-5\">https://doi.org/10.1007/s11005-025-01904-5</a>."},"quality_controlled":"1","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"_id":"19001","scopus_import":"1","OA_type":"hybrid","language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-02-05T07:01:40Z","abstract":[{"text":"We consider two Hamiltonians that are close to each other, H1≈H2, and analyze the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2 that expresses the effect of an imperfect time reversal on the initial state ψ0. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such H1 and H2.","lang":"eng"}],"ec_funded":1,"volume":115,"oa_version":"Published Version","pmid":1,"date_published":"2025-01-30T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","title":"Loschmidt echo for deformed Wigner matrices","article_processing_charge":"Yes (via OA deal)","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"first_name":"Oleksii","full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","orcid":"0000-0003-1491-4623"}],"acknowledgement":"We thank Giorgio Cipolloni for helpful discussions in a closely related joint project. Open access funding provided by Institute of Science and Technology (IST Austria). All authors were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","external_id":{"arxiv":["2410.08108"],"pmid":["39896265"],"isi":["001409618800002"]},"article_number":"14","ddc":["510"],"publication_identifier":{"issn":["1573-0530"]},"intvolume":"       115","month":"01","corr_author":"1","arxiv":1,"status":"public","has_accepted_license":"1","OA_place":"publisher","publication":"Letters in Mathematical Physics","publisher":"Springer Nature"},{"has_accepted_license":"1","status":"public","corr_author":"1","arxiv":1,"publisher":"EMS Press","publication":"Documenta Mathematica","OA_place":"publisher","publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"month":"03","intvolume":"        30","acknowledgement":"We thank Ping Zhong for pointing out references [15,19] and providing helpful comments. We also thank the anonymous referee for many valuable comments and proposals to streamline the presentation. This work was partially supported by ERC Advanced Grant “RMTBeyond” No. 10102033.","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"last_name":"Ji","first_name":"Hong Chang","full_name":"Ji, Hong Chang"}],"ddc":["510"],"external_id":{"arxiv":["2307.08626"],"isi":["001450119900005"]},"page":"417-453","year":"2025","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2025-03-20T00:00:00Z","oa_version":"Published Version","volume":30,"article_processing_charge":"Yes","title":"Density of Brown measure of free circular Brownian motion","OA_type":"gold","scopus_import":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider the Brown measure of the free circular Brownian motion,  a+t√x , with an arbitrary initial condition  a , i.e.  a  is a general non-normal operator and  x  is a circular element  ∗ -free from  a . We prove that, under a mild assumption on  a , the density of the Brown measure has one of the following two types of behavior around each point on the boundary of its support -- either (i) sharp cut, i.e. a jump discontinuity along the boundary, or (ii) quadratic decay at certain critical points on the boundary. Our result is in direct analogy with the previously known phenomenon for the spectral density of free semicircular Brownian motion, whose singularities are either a square-root edge or a cubic cusp. We also provide several examples and counterexamples, one of which shows that our assumption on  a  is necessary."}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-04-07T11:21:13Z","DOAJ_listed":"1","date_updated":"2025-09-30T11:28:02Z","citation":{"chicago":"Erdös, László, and Hong Chang Ji. “Density of Brown Measure of Free Circular Brownian Motion.” <i>Documenta Mathematica</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/DM/999\">https://doi.org/10.4171/DM/999</a>.","short":"L. Erdös, H.C. Ji, Documenta Mathematica 30 (2025) 417–453.","mla":"Erdös, László, and Hong Chang Ji. “Density of Brown Measure of Free Circular Brownian Motion.” <i>Documenta Mathematica</i>, vol. 30, no. 2, EMS Press, 2025, pp. 417–53, doi:<a href=\"https://doi.org/10.4171/DM/999\">10.4171/DM/999</a>.","ieee":"L. Erdös and H. C. Ji, “Density of Brown measure of free circular Brownian motion,” <i>Documenta Mathematica</i>, vol. 30, no. 2. EMS Press, pp. 417–453, 2025.","apa":"Erdös, L., &#38; Ji, H. C. (2025). Density of Brown measure of free circular Brownian motion. <i>Documenta Mathematica</i>. EMS Press. <a href=\"https://doi.org/10.4171/DM/999\">https://doi.org/10.4171/DM/999</a>","ama":"Erdös L, Ji HC. Density of Brown measure of free circular Brownian motion. <i>Documenta Mathematica</i>. 2025;30(2):417-453. doi:<a href=\"https://doi.org/10.4171/DM/999\">10.4171/DM/999</a>","ista":"Erdös L, Ji HC. 2025. Density of Brown measure of free circular Brownian motion. Documenta Mathematica. 30(2), 417–453."},"quality_controlled":"1","_id":"19500","issue":"2","publication_status":"published","date_created":"2025-04-06T22:01:32Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","doi":"10.4171/DM/999","department":[{"_id":"LaEr"}],"file":[{"creator":"dernst","date_created":"2025-04-07T11:21:13Z","file_size":1366865,"relation":"main_file","file_id":"19523","checksum":"97a02d18c05f2b9f2048747b140e7d43","access_level":"open_access","success":1,"date_updated":"2025-04-07T11:21:13Z","file_name":"2025_DocumentaMathematica_Erdoes.pdf","content_type":"application/pdf"}],"article_type":"original","day":"20","isi":1,"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}]},{"publication":"arXiv","OA_place":"repository","arxiv":1,"corr_author":"1","status":"public","month":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.10718"}],"external_id":{"arxiv":["2410.10718"]},"acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","first_name":"Oleksii","orcid":"0000-0003-1491-4623","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"title":"Eigenvector decorrelation for random matrices","article_processing_charge":"No","date_published":"2025-01-30T00:00:00Z","oa_version":"Preprint","year":"2025","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","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."}],"oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"_id":"19546","date_updated":"2026-04-07T12:37:11Z","citation":{"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>.","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>","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>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>arXiv</i>. .","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>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","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>."},"related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"doi":"10.48550/arXiv.2410.10718","department":[{"_id":"LaEr"}],"publication_status":"draft","date_created":"2025-04-11T08:34:49Z","type":"preprint","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"day":"30"},{"publication_status":"epub_ahead","date_created":"2025-05-25T22:16:59Z","type":"journal_article","doi":"10.1007/s00440-025-01384-7","department":[{"_id":"LaEr"}],"article_type":"original","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"day":"01","isi":1,"OA_type":"hybrid","scopus_import":"1","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":1,"ec_funded":1,"quality_controlled":"1","date_updated":"2026-06-18T18:17:57Z","citation":{"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>","ista":"Cipolloni G, Erdös L, Ji HC. 2025. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields., 050603.","short":"G. Cipolloni, L. Erdös, H.C. Ji, Probability Theory and Related Fields (2025).","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>.","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.","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>."},"_id":"19737","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Ji","full_name":"Ji, Hong Chang","first_name":"Hong Chang"}],"article_number":"050603","ddc":["500"],"external_id":{"isi":["001493091900001"]},"oa_version":"Published Version","date_published":"2025-01-01T00:00:00Z","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Non–Hermitian spectral universality at critical points","article_processing_charge":"Yes (via OA deal)","corr_author":"1","status":"public","publication":"Probability Theory and Related Fields","OA_place":"publisher","publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.1007/s00440-025-01384-7","open_access":"1"}],"publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"month":"01"},{"PlanS_conform":"1","isi":1,"day":"01","article_type":"original","file":[{"file_id":"20336","relation":"main_file","date_created":"2025-09-10T07:48:21Z","file_size":1465827,"creator":"dernst","content_type":"application/pdf","date_updated":"2025-09-10T07:48:21Z","file_name":"2025_CommMathPhysics_Erdoes.pdf","checksum":"abd32af7b8ca6dc5b9080823a433986b","access_level":"open_access","success":1}],"doi":"10.1007/s00220-025-05417-z","department":[{"_id":"LaEr"}],"type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"date_created":"2025-09-10T05:38:17Z","publication_status":"published","issue":"10","_id":"20322","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"19547"},{"relation":"dissertation_contains","id":"20575","status":"public"}]},"quality_controlled":"1","citation":{"ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 10. Springer Nature, 2025.","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 10, 253, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05417-z\">10.1007/s00220-025-05417-z</a>.","short":"L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025).","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00220-025-05417-z\">https://doi.org/10.1007/s00220-025-05417-z</a>.","ista":"Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253.","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. <i>Communications in Mathematical Physics</i>. 2025;406(10). doi:<a href=\"https://doi.org/10.1007/s00220-025-05417-z\">10.1007/s00220-025-05417-z</a>","apa":"Erdös, L., Henheik, S. J., &#38; Riabov, V. (2025). Cusp universality for correlated random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-025-05417-z\">https://doi.org/10.1007/s00220-025-05417-z</a>"},"date_updated":"2026-04-07T12:32:19Z","file_date_updated":"2025-09-10T07:48:21Z","oa":1,"language":[{"iso":"eng"}],"abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the <jats:italic>Zigzag strategy</jats:italic>, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.","lang":"eng"}],"scopus_import":"1","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","title":"Cusp universality for correlated random matrices","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2025","date_published":"2025-09-01T00:00:00Z","oa_version":"Published Version","volume":406,"external_id":{"isi":["001565019000005"],"arxiv":["2410.06813"]},"article_number":"253","ddc":["510"],"author":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr","full_name":"Riabov, Volodymyr","last_name":"Riabov"}],"acknowledgement":"We thank Giorgio Cipolloni for many productive discussions and the anonymous referees for several useful suggestions and spotting some typos. Open access funding provided by Institute of Science and Technology (IST Austria).","month":"09","intvolume":"       406","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"publisher":"Springer Nature","OA_place":"publisher","publication":"Communications in Mathematical Physics","status":"public","has_accepted_license":"1","arxiv":1,"corr_author":"1"},{"date_updated":"2026-06-18T18:23:40Z","quality_controlled":"1","citation":{"ista":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields.","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>","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.","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>."},"_id":"20478","OA_type":"hybrid","scopus_import":"1","ec_funded":1,"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."}],"oa":1,"language":[{"iso":"eng"}],"article_type":"original","day":"20","isi":1,"PlanS_conform":"1","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"date_created":"2025-10-16T13:10:26Z","publication_status":"epub_ahead","type":"journal_article","doi":"10.1007/s00440-025-01422-4","department":[{"_id":"LaEr"}],"main_file_link":[{"url":"https://doi.org/10.1007/s00440-025-01422-4","open_access":"1"}],"publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"month":"09","status":"public","corr_author":"1","arxiv":1,"publisher":"Springer Nature","publication":"Probability Theory and Related Fields","OA_place":"publisher","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","date_published":"2025-09-20T00:00:00Z","article_processing_charge":"Yes (via OA deal)","title":"Decorrelation transition in the Wigner minor process","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.","author":[{"orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","full_name":"Bao, Zhigang","first_name":"Zhigang"},{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"orcid":"0000-0003-1491-4623","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","last_name":"Kolupaiev","first_name":"Oleksii","full_name":"Kolupaiev, Oleksii"}],"ddc":["500"],"external_id":{"isi":["001574640900001"],"arxiv":["2503.06549"]}},{"doi":"10.48550/ARXIV.2506.06441","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publication_status":"draft","acknowledgement":" Supported by the ERC\r\nAdvanced Grant ”RMTBeyond” No. 101020331.","date_created":"2025-10-29T19:09:03Z","author":[{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr","full_name":"Riabov, Volodymyr","last_name":"Riabov"}],"type":"preprint","title":"The zigzag strategy for random band matrices","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"day":"06","article_processing_charge":"No","date_published":"2025-06-06T00:00:00Z","oa_version":"Preprint","year":"2025","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","abstract":[{"lang":"eng","text":"We prove that a very general class of $N\\times N$ Hermitian random band matrices is in the delocalized phase when the band width $W$ exceeds the critical threshold, $W\\gg \\sqrt{N}$. In this regime, we show that, in the bulk spectrum, the eigenfunctions are fully delocalized, the eigenvalues follow the universal Wigner-Dyson statistics, and quantum unique ergodicity holds for general diagonal observables with an optimal convergence rate. Our results are valid for general variance profiles, arbitrary single entry distributions, in both real-symmetric and complex-Hermitian symmetry classes. In particular, our work substantially generalizes the recent breakthrough result of Yau and Yin [arXiv:2501.01718], obtained for a specific complex Hermitian Gaussian block band matrix. The main technical input is the optimal multi-resolvent local laws -- both in the averaged and fully isotropic form. We also generalize the $\\sqrtη$-rule from [arXiv:2012.13215] to exploit the additional effect of traceless observables. Our analysis is based on the zigzag strategy, complemented with a new global-scale estimate derived using the static version of the master inequalities, while the zig-step and the a priori estimates on the deterministic approximations are proven dynamically."}],"publication":"arXiv","OA_place":"repository","language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"corr_author":"1","status":"public","_id":"20576","month":"06","citation":{"ama":"Erdös L, Riabov V. The zigzag strategy for random band matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">10.48550/ARXIV.2506.06441</a>","apa":"Erdös, L., &#38; Riabov, V. (n.d.). The zigzag strategy for random band matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">https://doi.org/10.48550/ARXIV.2506.06441</a>","ista":"Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">10.48550/ARXIV.2506.06441</a>.","short":"L. Erdös, V. Riabov, ArXiv (n.d.).","chicago":"Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">https://doi.org/10.48550/ARXIV.2506.06441</a>.","ieee":"L. Erdös and V. Riabov, “The zigzag strategy for random band matrices,” <i>arXiv</i>. .","mla":"Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">10.48550/ARXIV.2506.06441</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2506.06441"}],"date_updated":"2026-04-07T12:32:19Z","related_material":{"record":[{"status":"public","id":"20575","relation":"dissertation_contains"}]}},{"citation":{"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>","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>","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.","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>.","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.","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>."},"date_updated":"2025-08-05T13:28:15Z","quality_controlled":"1","_id":"14408","scopus_import":"1","ec_funded":1,"language":[{"iso":"eng"}],"oa":1,"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"}],"article_type":"original","isi":1,"day":"01","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","publication_status":"published","date_created":"2023-10-08T22:01:17Z","department":[{"_id":"LaEr"}],"doi":"10.1007/s00440-023-01229-1","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.12060","open_access":"1"}],"month":"04","intvolume":"       188","status":"public","arxiv":1,"publisher":"Springer Nature","publication":"Probability Theory and Related Fields","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","page":"1131-1182","date_published":"2024-04-01T00:00:00Z","volume":188,"oa_version":"Preprint","article_processing_charge":"No","title":"Mesoscopic central limit theorem for non-Hermitian random matrices","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J"}],"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.","external_id":{"isi":["001118972500001"],"arxiv":["2210.12060"]}},{"publication":"Annals of Applied Probability","publisher":"Institute of Mathematical Statistics","corr_author":"1","arxiv":1,"status":"public","intvolume":"        34","month":"02","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2208.12206"}],"publication_identifier":{"issn":["1050-5164"]},"external_id":{"arxiv":["2208.12206"],"isi":["001163006100021"]},"acknowledgement":"The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation.","author":[{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0003-2625-495X","id":"b0cc634c-d549-11ee-96c8-87338c7ad808","last_name":"McKenna","full_name":"McKenna, Benjamin","first_name":"Benjamin"}],"title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","article_processing_charge":"No","oa_version":"Preprint","volume":34,"date_published":"2024-02-01T00:00:00Z","year":"2024","page":"1623-1662","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","abstract":[{"text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble.","lang":"eng"}],"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"scopus_import":"1","_id":"15025","issue":"1B","quality_controlled":"1","citation":{"ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. 2024;34(1B):1623-1662. doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>","apa":"Erdös, L., &#38; McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>.","ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” <i>Annals of Applied Probability</i>, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>."},"date_updated":"2025-09-04T12:08:11Z","doi":"10.1214/23-AAP2000","department":[{"_id":"LaEr"}],"date_created":"2024-02-25T23:00:56Z","publication_status":"published","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"isi":1,"day":"01","article_type":"original"},{"article_processing_charge":"Yes (via OA deal)","title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","page":"3785-3840","year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-09-01T00:00:00Z","oa_version":"Published Version","volume":77,"ddc":["510"],"external_id":{"arxiv":["2301.04981"],"isi":["001217139900001"]},"acknowledgement":"László Erdős is partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Hong Chang Ji is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","author":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hong Chang","full_name":"Ji, Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"month":"09","intvolume":"        77","publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"publisher":"Wiley","publication":"Communications on Pure and Applied Mathematics","OA_place":"publisher","has_accepted_license":"1","status":"public","corr_author":"1","arxiv":1,"day":"01","isi":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"article_type":"original","department":[{"_id":"LaEr"}],"doi":"10.1002/cpa.22201","file":[{"creator":"dernst","date_created":"2025-01-09T09:36:41Z","file_size":566963,"relation":"main_file","file_id":"18803","checksum":"fbcc9cc7bf274f024e4f4afc9c208f96","success":1,"access_level":"open_access","date_updated":"2025-01-09T09:36:41Z","file_name":"2024_CommPureApplMath_Erdoes.pdf","content_type":"application/pdf"}],"publication_status":"published","date_created":"2024-05-12T22:01:02Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"type":"journal_article","issue":"9","_id":"15378","citation":{"ista":"Erdös L, Ji HC. 2024. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 77(9), 3785–3840.","apa":"Erdös, L., &#38; Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>","ama":"Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2024;77(9):3785-3840. doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>","mla":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>.","ieee":"L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024.","chicago":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2024. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>.","short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840."},"quality_controlled":"1","date_updated":"2025-09-08T07:25:47Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","abstract":[{"text":"We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest.","lang":"eng"}],"file_date_updated":"2025-01-09T09:36:41Z","oa":1,"language":[{"iso":"eng"}],"OA_type":"hybrid","scopus_import":"1"},{"date_created":"2024-05-26T22:00:57Z","publication_status":"published","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","doi":"10.1016/j.jfa.2024.110495","department":[{"_id":"LaEr"}],"file":[{"date_created":"2025-06-24T13:14:21Z","file_size":1374854,"creator":"dernst","relation":"main_file","file_id":"19891","date_updated":"2025-06-24T13:14:21Z","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","checksum":"07d3f73e0c56e68eb110851842c22ee0","success":1,"access_level":"open_access","content_type":"application/pdf"}],"article_type":"original","isi":1,"day":"15","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"OA_type":"hybrid","scopus_import":"1","ec_funded":1,"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2025-06-24T13:14:21Z","oa":1,"language":[{"iso":"eng"}],"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"citation":{"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>.","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.","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>","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."},"quality_controlled":"1","date_updated":"2026-04-07T12:37:11Z","issue":"4","_id":"17049","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"ddc":["510"],"article_number":"110495","external_id":{"isi":["001325502400001"]},"year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-08-15T00:00:00Z","oa_version":"Published Version","volume":287,"article_processing_charge":"Yes (via OA deal)","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","has_accepted_license":"1","status":"public","corr_author":"1","publisher":"Elsevier","publication":"Journal of Functional Analysis","OA_place":"publisher","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"month":"08","intvolume":"       287"},{"OA_type":"hybrid","scopus_import":"1","abstract":[{"text":"We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure.","lang":"eng"}],"oa":1,"language":[{"iso":"eng"}],"file_date_updated":"2024-11-18T08:15:07Z","related_material":{"record":[{"id":"20575","relation":"dissertation_contains","status":"public"}]},"citation":{"short":"L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).","chicago":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>.","ieee":"L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12. Springer Nature, 2024.","mla":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12, 282, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>.","ama":"Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. 2024;405(12). doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>","apa":"Erdös, L., &#38; Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>","ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282."},"quality_controlled":"1","date_updated":"2026-04-07T12:32:19Z","issue":"12","_id":"18554","publication_status":"published","date_created":"2024-11-17T23:01:46Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","doi":"10.1007/s00220-024-05143-y","department":[{"_id":"LaEr"}],"file":[{"file_id":"18562","relation":"main_file","creator":"dernst","date_created":"2024-11-18T08:15:07Z","file_size":1426046,"content_type":"application/pdf","checksum":"c9ae0ea195bd39b8b3a630d492fb00dc","access_level":"open_access","success":1,"date_updated":"2024-11-18T08:15:07Z","file_name":"2024_CommMathPhysics_Erdoes.pdf"}],"article_type":"original","isi":1,"day":"01","has_accepted_license":"1","status":"public","arxiv":1,"corr_author":"1","publisher":"Springer Nature","publication":"Communications in Mathematical Physics","OA_place":"publisher","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"month":"12","intvolume":"       405","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","author":[{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Volodymyr","full_name":"Riabov, Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"ddc":["510"],"article_number":"282","external_id":{"isi":["001348943900004"],"pmid":["39526190"],"arxiv":["2403.10359"]},"year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","date_published":"2024-12-01T00:00:00Z","volume":405,"pmid":1,"article_processing_charge":"Yes (via OA deal)","title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices"},{"acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"external_id":{"arxiv":["2309.05488"]},"date_published":"2024-12-17T00:00:00Z","oa_version":"Preprint","year":"2024","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"Eigenstate thermalisation at the edge for Wigner matrices","article_processing_charge":"No","arxiv":1,"corr_author":"1","status":"public","publication":"arXiv","OA_place":"repository","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.05488"}],"month":"12","publication_status":"draft","date_created":"2025-04-11T08:19:22Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"preprint","doi":"10.48550/arXiv.2309.05488","department":[{"_id":"LaEr"}],"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"day":"17","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."}],"oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"citation":{"ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. .","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>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","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>.","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>.","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>"},"date_updated":"2026-04-07T12:37:11Z","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"_id":"19545"},{"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"day":"03","type":"preprint","publication_status":"draft","date_created":"2025-04-11T08:48:21Z","doi":"10.48550/arXiv.2410.06813","department":[{"_id":"LaEr"}],"citation":{"chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>.","short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>.","ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>arXiv</i>. .","apa":"Erdös, L., Henheik, S. J., &#38; Riabov, V. (n.d.). Cusp universality for correlated random matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>","ista":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>."},"date_updated":"2026-04-07T12:37:11Z","related_material":{"record":[{"id":"20322","relation":"later_version","status":"public"},{"id":"20575","relation":"dissertation_contains","status":"public"},{"id":"19540","relation":"dissertation_contains","status":"public"}]},"_id":"19547","oa":1,"language":[{"iso":"eng"}],"abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes.","lang":"eng"}],"ec_funded":1,"oa_version":"Preprint","date_published":"2024-11-03T00:00:00Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","year":"2024","title":"Cusp universality for correlated random matrices","article_processing_charge":"No","author":[{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik"},{"last_name":"Riabov","first_name":"Volodymyr","full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","external_id":{"arxiv":["2410.06813"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.06813","open_access":"1"}],"month":"11","arxiv":1,"corr_author":"1","status":"public","OA_place":"repository","publication":"arXiv"},{"citation":{"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>.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","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>.","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.","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>","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>","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."},"quality_controlled":"1","date_updated":"2025-09-08T08:44:57Z","_id":"17375","issue":"6","scopus_import":"1","oa":1,"language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"article_type":"original","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"day":"01","isi":1,"type":"journal_article","publication_status":"published","date_created":"2024-08-04T22:01:22Z","department":[{"_id":"LaEr"}],"doi":"10.1063/5.0209705","publication_identifier":{"issn":["0022-2488"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.15643"}],"intvolume":"        65","month":"06","arxiv":1,"corr_author":"1","status":"public","publication":"Journal of Mathematical Physics","publisher":"AIP Publishing","oa_version":"Preprint","date_published":"2024-06-01T00:00:00Z","volume":65,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","title":"Precise asymptotics for the spectral radius of a large random matrix","article_processing_charge":"No","author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","external_id":{"isi":["001252240700002"],"arxiv":["2210.15643"]},"article_number":"063302"},{"date_updated":"2026-07-06T13:35:37Z","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.","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 of Boston. <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>","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 of Boston, 2024, pp. 2025–83, 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 of Boston, pp. 2025–2083, 2024.","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 of Boston, 2024. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083."},"quality_controlled":"1","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"_id":"18656","issue":"6","scopus_import":"1","OA_type":"green","oa":1,"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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])."}],"ec_funded":1,"article_type":"original","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"day":"30","type":"journal_article","publication_status":"published","date_created":"2024-12-15T23:01:51Z","department":[{"_id":"LaEr"}],"doi":"10.4310/ATMP.241031013250","publication_identifier":{"eissn":["1095-0753"],"issn":["1095-0761"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.17609"}],"intvolume":"        28","month":"10","corr_author":"1","arxiv":1,"status":"public","OA_place":"repository","publication":"Advances in Theoretical and Mathematical Physics","publisher":"International Press of Boston","das_tickbox":"1","volume":28,"oa_version":"Preprint","date_published":"2024-10-30T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","page":"2025-2083","title":"Out-of-time-ordered correlators for Wigner matrices","article_processing_charge":"No","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","external_id":{"arxiv":["2402.17609"]}}]