--- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20328' 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. acknowledgement: Partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Partially supported by National Key R&D Program of China No. 2024YFA1013503. article_number: '111180' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu orcid: 0000-0003-1559-1205 citation: ama: Cipolloni G, Erdös L, Xu Y. Optimal decay of eigenvector overlap for non-Hermitian random matrices. Journal of Functional Analysis. 2026;290(1). doi:10.1016/j.jfa.2025.111180 apa: Cipolloni, G., Erdös, L., & Xu, Y. (2026). Optimal decay of eigenvector overlap for non-Hermitian random matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2025.111180 chicago: Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” Journal of Functional Analysis. Elsevier, 2026. https://doi.org/10.1016/j.jfa.2025.111180. ieee: G. Cipolloni, L. Erdös, and Y. Xu, “Optimal decay of eigenvector overlap for non-Hermitian random matrices,” Journal of Functional Analysis, vol. 290, no. 1. Elsevier, 2026. 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. mla: Cipolloni, Giorgio, et al. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” Journal of Functional Analysis, vol. 290, no. 1, 111180, Elsevier, 2026, doi:10.1016/j.jfa.2025.111180. short: G. Cipolloni, L. Erdös, Y. Xu, Journal of Functional Analysis 290 (2026). corr_author: '1' date_created: 2025-09-10T05:46:07Z date_published: 2026-01-01T00:00:00Z date_updated: 2026-06-03T13:12:14Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1016/j.jfa.2025.111180 ec_funded: 1 external_id: arxiv: - '2411.16572' isi: - '001583178200001' oaworkid: - w4413883397 file: - access_level: open_access checksum: ee53d5e695f0df11e017c8c9242a2b04 content_type: application/pdf creator: dernst date_created: 2026-01-05T13:05:47Z date_updated: 2026-01-05T13:05:47Z file_id: '20947' file_name: 2026_JourFuncAnalysis_Cipolloni.pdf file_size: 2503887 relation: main_file success: 1 file_date_updated: 2026-01-05T13:05:47Z has_accepted_license: '1' intvolume: ' 290' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version oaworkid: 1 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Functional Analysis publication_identifier: issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Optimal decay of eigenvector overlap for non-Hermitian random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 290 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20925' 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.' 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). article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Cornelia full_name: Vogel, Cornelia id: 1cd0554a-ea28-11f0-9f40-ff76440883cd last_name: Vogel citation: ama: Erdös L, Henheik SJ, Vogel C. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 2025;116. doi:10.1007/s11005-025-02037-5 apa: Erdös, L., Henheik, S. J., & Vogel, C. (2025). Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-02037-5 chicago: Erdös, László, Sven Joscha Henheik, and Cornelia Vogel. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” Letters in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s11005-025-02037-5. ieee: L. Erdös, S. J. Henheik, and C. Vogel, “Normal typicality and dynamical typicality for a random block-band matrix model,” Letters in Mathematical Physics, vol. 116. Springer Nature, 2025. 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. mla: Erdös, László, et al. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” Letters in Mathematical Physics, vol. 116, 5, Springer Nature, 2025, doi:10.1007/s11005-025-02037-5. short: L. Erdös, S.J. Henheik, C. Vogel, Letters in Mathematical Physics 116 (2025). corr_author: '1' date_created: 2026-01-04T23:01:33Z date_published: 2025-12-26T00:00:00Z date_updated: 2026-01-05T11:22:25Z day: '26' ddc: - '510' department: - _id: LaEr doi: 10.1007/s11005-025-02037-5 ec_funded: 1 external_id: pmid: - '41459414' has_accepted_license: '1' intvolume: ' 116' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s11005-025-02037-5 month: '12' oa: 1 oa_version: Published Version pmid: 1 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Normal typicality and dynamical typicality for a random block-band matrix model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 116 year: '2025' ... --- OA_place: repository OA_type: green _id: '21271' 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. 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Andrew J full_name: Campbell, Andrew J id: 582b06a9-1f1c-11ee-b076-82ffce00dde4 last_name: Campbell - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji citation: ama: Campbell AJ, Cipolloni G, Erdös L, Ji HC. On the spectral edge of non-Hermitian random matrices. The Annals of Probability. 2025;53(6):2256-2308. doi:10.1214/25-aop1761 apa: Campbell, A. J., Cipolloni, G., Erdös, L., & Ji, H. C. (2025). On the spectral edge of non-Hermitian random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aop1761 chicago: Campbell, Andrew J, Giorgio Cipolloni, László Erdös, and Hong Chang Ji. “On the Spectral Edge of Non-Hermitian Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/25-aop1761. ieee: A. J. Campbell, G. Cipolloni, L. Erdös, and H. C. Ji, “On the spectral edge of non-Hermitian random matrices,” The Annals of Probability, vol. 53, no. 6. Institute of Mathematical Statistics, pp. 2256–2308, 2025. 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. mla: Campbell, Andrew J., et al. “On the Spectral Edge of Non-Hermitian Random Matrices.” The Annals of Probability, vol. 53, no. 6, Institute of Mathematical Statistics, 2025, pp. 2256–308, doi:10.1214/25-aop1761. short: A.J. Campbell, G. Cipolloni, L. Erdös, H.C. Ji, The Annals of Probability 53 (2025) 2256–2308. corr_author: '1' date_created: 2026-02-17T07:58:20Z date_published: 2025-11-01T00:00:00Z date_updated: 2026-02-18T08:35:38Z day: '01' department: - _id: LaEr doi: 10.1214/25-aop1761 ec_funded: 1 external_id: arxiv: - '2404.17512' intvolume: ' 53' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2404.17512 month: '11' oa: 1 oa_version: Preprint page: 2256-2308 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: The Annals of Probability publication_identifier: eissn: - 2168-894X issn: - 0091-1798 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' status: public title: On the spectral edge of non-Hermitian random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 53 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18764' abstract: - lang: eng 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. 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)." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 2025;26:1991-2033. doi:10.1007/s00023-024-01518-y apa: Erdös, L., Henheik, S. J., Reker, J., & Riabov, V. (2025). Prethermalization for deformed Wigner matrices. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-024-01518-y chicago: Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” Annales Henri Poincare. Springer Nature, 2025. https://doi.org/10.1007/s00023-024-01518-y. ieee: L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner matrices,” Annales Henri Poincare, vol. 26. Springer Nature, pp. 1991–2033, 2025. ista: Erdös L, Henheik SJ, Reker J, Riabov V. 2025. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 26, 1991–2033. mla: Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” Annales Henri Poincare, vol. 26, Springer Nature, 2025, pp. 1991–2033, doi:10.1007/s00023-024-01518-y. short: L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025) 1991–2033. corr_author: '1' date_created: 2025-01-05T23:01:59Z date_published: 2025-06-01T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00023-024-01518-y ec_funded: 1 external_id: arxiv: - '2310.06677' isi: - '001385326500001' file: - access_level: open_access checksum: 49e6a934db540206f7eaa0c798553ded content_type: application/pdf creator: dernst date_created: 2025-06-25T05:38:34Z date_updated: 2025-06-25T05:38:34Z file_id: '19895' file_name: 2025_AnnalesHenriPoincare_Erdoes.pdf file_size: 977773 relation: main_file success: 1 file_date_updated: 2025-06-25T05:38:34Z has_accepted_license: '1' intvolume: ' 26' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1991-2033 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '17174' relation: earlier_version status: public - id: '20575' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Prethermalization for deformed Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 26 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19001' abstract: - lang: eng 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. 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. article_number: '14' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev orcid: 0000-0003-1491-4623 citation: ama: Erdös L, Henheik SJ, Kolupaiev O. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 2025;115. doi:10.1007/s11005-025-01904-5 apa: Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025). Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-01904-5 chicago: Erdös, László, Sven Joscha Henheik, and Oleksii Kolupaiev. “Loschmidt Echo for Deformed Wigner Matrices.” Letters in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s11005-025-01904-5. ieee: L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner matrices,” Letters in Mathematical Physics, vol. 115. Springer Nature, 2025. ista: Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 115, 14. mla: Erdös, László, et al. “Loschmidt Echo for Deformed Wigner Matrices.” Letters in Mathematical Physics, vol. 115, 14, Springer Nature, 2025, doi:10.1007/s11005-025-01904-5. short: L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115 (2025). corr_author: '1' date_created: 2025-02-05T06:48:29Z date_published: 2025-01-30T00:00:00Z date_updated: 2026-04-07T12:37:10Z day: '30' ddc: - '510' department: - _id: LaEr doi: 10.1007/s11005-025-01904-5 ec_funded: 1 external_id: arxiv: - '2410.08108' isi: - '001409618800002' pmid: - '39896265' file: - access_level: open_access checksum: ee07edf5f85a6f2651926b2f8760af74 content_type: application/pdf creator: dernst date_created: 2025-02-05T07:01:40Z date_updated: 2025-02-05T07:01:40Z file_id: '19004' file_name: 2025_LettersMathPhysics_Erdoes.pdf file_size: 828335 relation: main_file success: 1 file_date_updated: 2025-02-05T07:01:40Z has_accepted_license: '1' intvolume: ' 115' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version pmid: 1 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Letters in Mathematical Physics publication_identifier: issn: - 1573-0530 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Loschmidt echo for deformed Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 115 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '19500' 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. 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. article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Hong Chang full_name: Ji, Hong Chang last_name: Ji citation: ama: Erdös L, Ji HC. Density of Brown measure of free circular Brownian motion. Documenta Mathematica. 2025;30(2):417-453. doi:10.4171/DM/999 apa: Erdös, L., & Ji, H. C. (2025). Density of Brown measure of free circular Brownian motion. Documenta Mathematica. EMS Press. https://doi.org/10.4171/DM/999 chicago: Erdös, László, and Hong Chang Ji. “Density of Brown Measure of Free Circular Brownian Motion.” Documenta Mathematica. EMS Press, 2025. https://doi.org/10.4171/DM/999. ieee: L. Erdös and H. C. Ji, “Density of Brown measure of free circular Brownian motion,” Documenta Mathematica, vol. 30, no. 2. EMS Press, pp. 417–453, 2025. ista: Erdös L, Ji HC. 2025. Density of Brown measure of free circular Brownian motion. Documenta Mathematica. 30(2), 417–453. mla: Erdös, László, and Hong Chang Ji. “Density of Brown Measure of Free Circular Brownian Motion.” Documenta Mathematica, vol. 30, no. 2, EMS Press, 2025, pp. 417–53, doi:10.4171/DM/999. short: L. Erdös, H.C. Ji, Documenta Mathematica 30 (2025) 417–453. corr_author: '1' date_created: 2025-04-06T22:01:32Z date_published: 2025-03-20T00:00:00Z date_updated: 2025-09-30T11:28:02Z day: '20' ddc: - '510' department: - _id: LaEr doi: 10.4171/DM/999 ec_funded: 1 external_id: arxiv: - '2307.08626' isi: - '001450119900005' file: - access_level: open_access checksum: 97a02d18c05f2b9f2048747b140e7d43 content_type: application/pdf creator: dernst date_created: 2025-04-07T11:21:13Z date_updated: 2025-04-07T11:21:13Z file_id: '19523' file_name: 2025_DocumentaMathematica_Erdoes.pdf file_size: 1366865 relation: main_file success: 1 file_date_updated: 2025-04-07T11:21:13Z has_accepted_license: '1' intvolume: ' 30' isi: 1 issue: '2' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 417-453 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Documenta Mathematica publication_identifier: eissn: - 1431-0643 issn: - 1431-0635 publication_status: published publisher: EMS Press quality_controlled: '1' scopus_import: '1' status: public title: Density of Brown measure of free circular Brownian motion tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 30 year: '2025' ... --- OA_place: repository _id: '19546' 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." acknowledgement: Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev orcid: 0000-0003-1491-4623 citation: ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv. doi:10.48550/arXiv.2410.10718 apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (n.d.). Eigenvector decorrelation for random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.10718 chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10718. ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” arXiv. . ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, 10.48550/arXiv.2410.10718. mla: Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.10718. short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:34:49Z date_published: 2025-01-30T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '30' department: - _id: LaEr doi: 10.48550/arXiv.2410.10718 ec_funded: 1 external_id: arxiv: - '2410.10718' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.10718 month: '01' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Eigenvector decorrelation for random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19737' 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. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). Supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_number: '050603' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Hong Chang full_name: Ji, Hong Chang last_name: Ji citation: ama: Cipolloni G, Erdös L, Ji HC. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields. 2025. doi:10.1007/s00440-025-01384-7 apa: Cipolloni, G., Erdös, L., & Ji, H. C. (2025). Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01384-7 chicago: Cipolloni, Giorgio, László Erdös, and Hong Chang Ji. “Non–Hermitian Spectral Universality at Critical Points.” Probability Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01384-7. ieee: G. Cipolloni, L. Erdös, and H. C. Ji, “Non–Hermitian spectral universality at critical points,” Probability Theory and Related Fields. Springer Nature, 2025. ista: Cipolloni G, Erdös L, Ji HC. 2025. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields., 050603. mla: Cipolloni, Giorgio, et al. “Non–Hermitian Spectral Universality at Critical Points.” Probability Theory and Related Fields, 050603, Springer Nature, 2025, doi:10.1007/s00440-025-01384-7. short: G. Cipolloni, L. Erdös, H.C. Ji, Probability Theory and Related Fields (2025). corr_author: '1' date_created: 2025-05-25T22:16:59Z date_published: 2025-01-01T00:00:00Z date_updated: 2026-06-18T18:17:57Z day: '01' ddc: - '500' department: - _id: LaEr doi: 10.1007/s00440-025-01384-7 ec_funded: 1 external_id: isi: - '001493091900001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00440-025-01384-7 month: '01' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Non–Hermitian spectral universality at critical points type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20322' abstract: - lang: eng 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 Zigzag strategy, 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. 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). article_number: '253' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 2025;406(10). doi:10.1007/s00220-025-05417-z apa: Erdös, L., Henheik, S. J., & Riabov, V. (2025). Cusp universality for correlated random matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-025-05417-z chicago: Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” Communications in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s00220-025-05417-z. ieee: L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” Communications in Mathematical Physics, vol. 406, no. 10. Springer Nature, 2025. ista: Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253. mla: Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” Communications in Mathematical Physics, vol. 406, no. 10, 253, Springer Nature, 2025, doi:10.1007/s00220-025-05417-z. short: L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025). corr_author: '1' date_created: 2025-09-10T05:38:17Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-04-07T12:32:19Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-025-05417-z external_id: arxiv: - '2410.06813' isi: - '001565019000005' file: - access_level: open_access checksum: abd32af7b8ca6dc5b9080823a433986b content_type: application/pdf creator: dernst date_created: 2025-09-10T07:48:21Z date_updated: 2025-09-10T07:48:21Z file_id: '20336' file_name: 2025_CommMathPhysics_Erdoes.pdf file_size: 1465827 relation: main_file success: 1 file_date_updated: 2025-09-10T07:48:21Z has_accepted_license: '1' intvolume: ' 406' isi: 1 issue: '10' language: - iso: eng month: '09' oa: 1 oa_version: Published Version publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '19547' relation: earlier_version status: public - id: '20575' relation: dissertation_contains status: public scopus_import: '1' status: public title: Cusp universality for correlated random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 406 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20478' 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.' 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev orcid: 0000-0003-1491-4623 citation: ama: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. 2025. doi:10.1007/s00440-025-01422-4 apa: Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025). Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01422-4 chicago: Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” Probability Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01422-4. ieee: Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation transition in the Wigner minor process,” Probability Theory and Related Fields. Springer Nature, 2025. ista: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. mla: Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.” Probability Theory and Related Fields, Springer Nature, 2025, doi:10.1007/s00440-025-01422-4. short: Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025). corr_author: '1' date_created: 2025-10-16T13:10:26Z date_published: 2025-09-20T00:00:00Z date_updated: 2026-06-18T18:23:40Z day: '20' ddc: - '500' department: - _id: LaEr doi: 10.1007/s00440-025-01422-4 ec_funded: 1 external_id: arxiv: - '2503.06549' isi: - '001574640900001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00440-025-01422-4 month: '09' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Decorrelation transition in the Wigner minor process type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: repository _id: '20576' 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. acknowledgement: " Supported by the ERC\r\nAdvanced Grant ”RMTBeyond” No. 101020331." article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv. doi:10.48550/ARXIV.2506.06441 apa: Erdös, L., & Riabov, V. (n.d.). The zigzag strategy for random band matrices. arXiv. https://doi.org/10.48550/ARXIV.2506.06441 chicago: Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2506.06441. ieee: L. Erdös and V. Riabov, “The zigzag strategy for random band matrices,” arXiv. . ista: Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv, 10.48550/ARXIV.2506.06441. mla: Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” ArXiv, doi:10.48550/ARXIV.2506.06441. short: L. Erdös, V. Riabov, ArXiv (n.d.). corr_author: '1' date_created: 2025-10-29T19:09:03Z date_published: 2025-06-06T00:00:00Z date_updated: 2026-04-07T12:32:19Z day: '06' department: - _id: GradSch - _id: LaEr doi: 10.48550/ARXIV.2506.06441 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2506.06441 month: '06' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '20575' relation: dissertation_contains status: public status: public title: The zigzag strategy for random band matrices type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2025' ... --- _id: '14408' abstract: - lang: eng text: "We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0Probability Theory and Related Fields. 2024;188:1131-1182. doi:10.1007/s00440-023-01229-1 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01229-1. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” Probability Theory and Related Fields, vol. 188. Springer Nature, pp. 1131–1182, 2024. 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. mla: Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:10.1007/s00440-023-01229-1. short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182. date_created: 2023-10-08T22:01:17Z date_published: 2024-04-01T00:00:00Z date_updated: 2025-08-05T13:28:15Z day: '01' department: - _id: LaEr doi: 10.1007/s00440-023-01229-1 ec_funded: 1 external_id: arxiv: - '2210.12060' isi: - '001118972500001' intvolume: ' 188' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2210.12060 month: '04' oa: 1 oa_version: Preprint page: 1131-1182 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Mesoscopic central limit theorem for non-Hermitian random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 188 year: '2024' ... --- _id: '15025' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Benjamin full_name: McKenna, Benjamin id: b0cc634c-d549-11ee-96c8-87338c7ad808 last_name: McKenna orcid: 0000-0003-2625-495X citation: ama: Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 2024;34(1B):1623-1662. doi:10.1214/23-AAP2000 apa: Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2000 chicago: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000. ieee: L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024. ista: Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662. mla: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000. short: L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662. corr_author: '1' date_created: 2024-02-25T23:00:56Z date_published: 2024-02-01T00:00:00Z date_updated: 2025-09-04T12:08:11Z day: '01' department: - _id: LaEr doi: 10.1214/23-AAP2000 ec_funded: 1 external_id: arxiv: - '2208.12206' isi: - '001163006100021' intvolume: ' 34' isi: 1 issue: 1B language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2208.12206 month: '02' oa: 1 oa_version: Preprint page: 1623-1662 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Annals of Applied Probability publication_identifier: issn: - 1050-5164 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Extremal statistics of quadratic forms of GOE/GUE eigenvectors type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 34 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15378' abstract: - lang: eng 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. 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji citation: ama: Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 2024;77(9):3785-3840. doi:10.1002/cpa.22201 apa: Erdös, L., & Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22201 chicago: Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics. Wiley, 2024. https://doi.org/10.1002/cpa.22201. ieee: L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024. 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. mla: Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:10.1002/cpa.22201. short: L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840. corr_author: '1' date_created: 2024-05-12T22:01:02Z date_published: 2024-09-01T00:00:00Z date_updated: 2025-09-08T07:25:47Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1002/cpa.22201 ec_funded: 1 external_id: arxiv: - '2301.04981' isi: - '001217139900001' file: - access_level: open_access checksum: fbcc9cc7bf274f024e4f4afc9c208f96 content_type: application/pdf creator: dernst date_created: 2025-01-09T09:36:41Z date_updated: 2025-01-09T09:36:41Z file_id: '18803' file_name: 2024_CommPureApplMath_Erdoes.pdf file_size: 566963 relation: main_file success: 1 file_date_updated: 2025-01-09T09:36:41Z has_accepted_license: '1' intvolume: ' 77' isi: 1 issue: '9' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 3785-3840 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Communications on Pure and Applied Mathematics publication_identifier: eissn: - 1097-0312 issn: - 0010-3640 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode 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 user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 77 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '17049' 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. acknowledgement: "Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089." article_number: '110495' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 2024;287(4). doi:10.1016/j.jfa.2024.110495 apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110495 chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110495. ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” Journal of Functional Analysis, vol. 287, no. 4. Elsevier, 2024. 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. mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” Journal of Functional Analysis, vol. 287, no. 4, 110495, Elsevier, 2024, doi:10.1016/j.jfa.2024.110495. short: G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024). corr_author: '1' date_created: 2024-05-26T22:00:57Z date_published: 2024-08-15T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '15' ddc: - '510' department: - _id: LaEr doi: 10.1016/j.jfa.2024.110495 ec_funded: 1 external_id: isi: - '001325502400001' file: - access_level: open_access checksum: 07d3f73e0c56e68eb110851842c22ee0 content_type: application/pdf creator: dernst date_created: 2025-06-24T13:14:21Z date_updated: 2025-06-24T13:14:21Z file_id: '19891' file_name: 2025_JourFunctionalAnalysis_Cipolloni.pdf file_size: 1374854 relation: main_file success: 1 file_date_updated: 2025-06-24T13:14:21Z has_accepted_license: '1' intvolume: ' 287' isi: 1 issue: '4' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 287 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '18554' abstract: - lang: eng 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. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). article_number: '282' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 2024;405(12). doi:10.1007/s00220-024-05143-y apa: Erdös, L., & Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-024-05143-y chicago: Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” Communications in Mathematical Physics. Springer Nature, 2024. https://doi.org/10.1007/s00220-024-05143-y. ieee: L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” Communications in Mathematical Physics, vol. 405, no. 12. Springer Nature, 2024. ista: Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282. mla: Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” Communications in Mathematical Physics, vol. 405, no. 12, 282, Springer Nature, 2024, doi:10.1007/s00220-024-05143-y. short: L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024). corr_author: '1' date_created: 2024-11-17T23:01:46Z date_published: 2024-12-01T00:00:00Z date_updated: 2026-04-07T12:32:19Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-024-05143-y external_id: arxiv: - '2403.10359' isi: - '001348943900004' pmid: - '39526190' file: - access_level: open_access checksum: c9ae0ea195bd39b8b3a630d492fb00dc content_type: application/pdf creator: dernst date_created: 2024-11-18T08:15:07Z date_updated: 2024-11-18T08:15:07Z file_id: '18562' file_name: 2024_CommMathPhysics_Erdoes.pdf file_size: 1426046 relation: main_file success: 1 file_date_updated: 2024-11-18T08:15:07Z has_accepted_license: '1' intvolume: ' 405' isi: 1 issue: '12' language: - iso: eng month: '12' oa: 1 oa_version: Published Version pmid: 1 publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '20575' relation: dissertation_contains status: public scopus_import: '1' status: public title: Eigenstate Thermalization Hypothesis for Wigner-type matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 405 year: '2024' ... --- OA_place: repository _id: '19545' 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." acknowledgement: Supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv. doi:10.48550/arXiv.2309.05488 apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. arXiv. https://doi.org/10.48550/arXiv.2309.05488 chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.05488. ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” arXiv. . ista: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, 10.48550/arXiv.2309.05488. mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” ArXiv, doi:10.48550/arXiv.2309.05488. short: G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:19:22Z date_published: 2024-12-17T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '17' department: - _id: LaEr doi: 10.48550/arXiv.2309.05488 ec_funded: 1 external_id: arxiv: - '2309.05488' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2309.05488 month: '12' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Eigenstate thermalisation at the edge for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '19547' abstract: - lang: eng 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." acknowledgement: "Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331." article_processing_charge: No arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv. doi:10.48550/arXiv.2410.06813 apa: Erdös, L., Henheik, S. J., & Riabov, V. (n.d.). Cusp universality for correlated random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.06813 chicago: Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.06813. ieee: L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” arXiv. . ista: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, 10.48550/arXiv.2410.06813. mla: Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.06813. short: L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:48:21Z date_published: 2024-11-03T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '03' department: - _id: LaEr doi: 10.48550/arXiv.2410.06813 ec_funded: 1 external_id: arxiv: - '2410.06813' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.06813 month: '11' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '20322' relation: later_version status: public - id: '20575' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public status: public title: Cusp universality for correlated random matrices type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- _id: '17375' 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. acknowledgement: L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331. article_number: '063302' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu orcid: 0000-0003-1559-1205 citation: ama: Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 2024;65(6). doi:10.1063/5.0209705 apa: Cipolloni, G., Erdös, L., & Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0209705 chicago: Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” Journal of Mathematical Physics. AIP Publishing, 2024. https://doi.org/10.1063/5.0209705. ieee: G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” Journal of Mathematical Physics, vol. 65, no. 6. AIP Publishing, 2024. 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.” Journal of Mathematical Physics, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:10.1063/5.0209705. short: G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024). corr_author: '1' date_created: 2024-08-04T22:01:22Z date_published: 2024-06-01T00:00:00Z date_updated: 2025-09-08T08:44:57Z day: '01' department: - _id: LaEr doi: 10.1063/5.0209705 ec_funded: 1 external_id: arxiv: - '2210.15643' isi: - '001252240700002' intvolume: ' 65' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2210.15643 month: '06' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Mathematical Physics publication_identifier: issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Precise asymptotics for the spectral radius of a large random matrix type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 65 year: '2024' ... --- OA_place: repository OA_type: green _id: '18656' 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])." acknowledgement: LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331 article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 2024;28(6):2025-2083. doi:10.4310/ATMP.241031013250 apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. International Press of Boston. https://doi.org/10.4310/ATMP.241031013250 chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics. International Press of Boston, 2024. https://doi.org/10.4310/ATMP.241031013250. ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6. International Press of Boston, pp. 2025–2083, 2024. 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. mla: Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6, International Press of Boston, 2024, pp. 2025–83, doi:10.4310/ATMP.241031013250. short: G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083. corr_author: '1' das_tickbox: '1' date_created: 2024-12-15T23:01:51Z date_published: 2024-10-30T00:00:00Z date_updated: 2026-07-06T13:35:37Z day: '30' department: - _id: LaEr doi: 10.4310/ATMP.241031013250 ec_funded: 1 external_id: arxiv: - '2402.17609' intvolume: ' 28' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2402.17609 month: '10' oa: 1 oa_version: Preprint page: 2025-2083 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Advances in Theoretical and Mathematical Physics publication_identifier: eissn: - 1095-0753 issn: - 1095-0761 publication_status: published publisher: International Press of Boston quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Out-of-time-ordered correlators for Wigner matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2024' ...