--- 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: 2026-01-05T13:05:52Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1016/j.jfa.2025.111180 ec_funded: 1 external_id: arxiv: - '2411.16572' isi: - '001583178200001' 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 license: https://creativecommons.org/licenses/by/4.0/ 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: 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' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '20046' abstract: - lang: eng text: A Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We investigate the limiting distribution of the largest eigenvalues of a Laplacian random matrix with Gaussian entries. Unlike many classical matrix ensembles, this random matrix model contains dependent entries. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics. In particular, after properly shifting and scaling, we show that the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. While the largest diagonal entry is also shown to have Gumbel fluctuations, there is a rather surprising difference between its deterministic centering term and the centering term required for the largest eigenvalues. acknowledgement: "The authors thank Santiago Arenas-Velilla and Victor Pérez-Abreu for comments on an earlier draft of this manuscript and for contributing Appendix A. The authors also thank Yan Fyodorov for providing useful references.\r\nA. Campbell was partially supported by the European Research Council Grant No. 101020331. K. Luh was supported in part by the Ralph E. Powe Junior Faculty Enhancement Award and Simons Foundation Grant MP-TSM-00001988. S. O’Rourke has been supported in part by NSF CAREER grant DMS-2143142. " article_processing_charge: Yes 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: Kyle full_name: Luh, Kyle last_name: Luh - first_name: Sean full_name: O’Rourke, Sean last_name: O’Rourke - first_name: Santiago full_name: Arenas-Velilla, Santiago last_name: Arenas-Velilla - first_name: Victor full_name: Perez-Abreu, Victor last_name: Perez-Abreu citation: ama: Campbell AJ, Luh K, O’Rourke S, Arenas-Velilla S, Perez-Abreu V. Extreme eigenvalues of Laplacian random matrices with Gaussian entries. Electronic Journal of Probability. 2025;30:1-52. doi:10.1214/25-ejp1366 apa: Campbell, A. J., Luh, K., O’Rourke, S., Arenas-Velilla, S., & Perez-Abreu, V. (2025). Extreme eigenvalues of Laplacian random matrices with Gaussian entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-ejp1366 chicago: Campbell, Andrew J, Kyle Luh, Sean O’Rourke, Santiago Arenas-Velilla, and Victor Perez-Abreu. “Extreme Eigenvalues of Laplacian Random Matrices with Gaussian Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/25-ejp1366. ieee: A. J. Campbell, K. Luh, S. O’Rourke, S. Arenas-Velilla, and V. Perez-Abreu, “Extreme eigenvalues of Laplacian random matrices with Gaussian entries,” Electronic Journal of Probability, vol. 30. Institute of Mathematical Statistics, pp. 1–52, 2025. ista: Campbell AJ, Luh K, O’Rourke S, Arenas-Velilla S, Perez-Abreu V. 2025. Extreme eigenvalues of Laplacian random matrices with Gaussian entries. Electronic Journal of Probability. 30, 1–52. mla: Campbell, Andrew J., et al. “Extreme Eigenvalues of Laplacian Random Matrices with Gaussian Entries.” Electronic Journal of Probability, vol. 30, Institute of Mathematical Statistics, 2025, pp. 1–52, doi:10.1214/25-ejp1366. short: A.J. Campbell, K. Luh, S. O’Rourke, S. Arenas-Velilla, V. Perez-Abreu, Electronic Journal of Probability 30 (2025) 1–52. corr_author: '1' date_created: 2025-07-21T08:06:18Z date_published: 2025-06-27T00:00:00Z date_updated: 2025-09-30T14:07:19Z day: '27' ddc: - '510' department: - _id: LaEr doi: 10.1214/25-ejp1366 ec_funded: 1 external_id: arxiv: - '2211.17175' isi: - '001540927000024' file: - access_level: open_access checksum: a7a9f2bb7a6295786c16d4c7bd612621 content_type: application/pdf creator: dernst date_created: 2025-07-23T08:35:53Z date_updated: 2025-07-23T08:35:53Z file_id: '20069' file_name: 2025_ElectronJourProbab_Campbell.pdf file_size: 580591 relation: main_file success: 1 file_date_updated: 2025-07-23T08:35:53Z has_accepted_license: '1' intvolume: ' 30' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1-52 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Electronic Journal of Probability publication_identifier: eissn: - 1083-6489 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' status: public title: Extreme eigenvalues of Laplacian random matrices with Gaussian entries 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: 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: 2025-12-01T15:01:39Z day: '20' 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 OA_type: green _id: '18880' abstract: - lang: eng text: In this paper, we provide a rate of convergence for a version of the Carathéodory convergence for the multiple SLE model with a Dyson Brownian motion driver towards its hydrodynamic limit, for β=1 and β=2. The results are obtained by combining techniques from the field of Schramm–Loewner Evolutions with modern techniques from random matrices. Our approach shows how one can apply modern tools used in the proof of universality in random matrix theory to the field of Schramm–Loewner Evolutions. article_number: '2450028' 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: Kyle full_name: Luh, Kyle last_name: Luh - first_name: Vlad full_name: Margarint, Vlad last_name: Margarint citation: ama: 'Campbell AJ, Luh K, Margarint V. Rate of convergence in multiple SLE using random matrix theory. Random Matrices: Theory and Application. 2025;14(1). doi:10.1142/S201032632450028X' apa: 'Campbell, A. J., Luh, K., & Margarint, V. (2025). Rate of convergence in multiple SLE using random matrix theory. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S201032632450028X' chicago: 'Campbell, Andrew J, Kyle Luh, and Vlad Margarint. “Rate of Convergence in Multiple SLE Using Random Matrix Theory.” Random Matrices: Theory and Application. World Scientific Publishing, 2025. https://doi.org/10.1142/S201032632450028X.' ieee: 'A. J. Campbell, K. Luh, and V. Margarint, “Rate of convergence in multiple SLE using random matrix theory,” Random Matrices: Theory and Application, vol. 14, no. 1. World Scientific Publishing, 2025.' ista: 'Campbell AJ, Luh K, Margarint V. 2025. Rate of convergence in multiple SLE using random matrix theory. Random Matrices: Theory and Application. 14(1), 2450028.' mla: 'Campbell, Andrew J., et al. “Rate of Convergence in Multiple SLE Using Random Matrix Theory.” Random Matrices: Theory and Application, vol. 14, no. 1, 2450028, World Scientific Publishing, 2025, doi:10.1142/S201032632450028X.' short: 'A.J. Campbell, K. Luh, V. Margarint, Random Matrices: Theory and Application 14 (2025).' date_created: 2025-01-26T23:01:49Z date_published: 2025-01-01T00:00:00Z date_updated: 2025-07-10T11:51:29Z day: '01' department: - _id: LaEr doi: 10.1142/S201032632450028X external_id: arxiv: - '2301.04722' isi: - '001397136000001' intvolume: ' 14' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2301.04722 month: '01' oa: 1 oa_version: Preprint publication: 'Random Matrices: Theory and Application' publication_identifier: eissn: - 2010-3271 issn: - 2010-3263 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Rate of convergence in multiple SLE using random matrix theory type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2025' ... --- OA_place: repository OA_type: green _id: '19039' abstract: - lang: eng text: "We consider fluctuations of the largest eigenvalues of the random matrix model A + UBU∗ where A and B are N × N deterministic Hermitian (or symmetric) matrices and U is a Haar-distributed unitary (or orthogonal) matrix. We prove that the largest eigenvalue weakly converges to the GUE (or GOE) Tracy–Widom distribution, under mild assumptions on A and B to\r\nguarantee that the density of states of the model decays as square root around\r\nthe upper edge. Our proof is based on the comparison of the Green function\r\nalong the Dyson Brownian motion starting from the matrix A + UBU∗ and\r\nending at time N−1/3+o(1). As a byproduct of our proof, we also prove an\r\noptimal local law for the Dyson Brownian motion up to the constant time\r\nscale." acknowledgement: The work of H.C. Ji was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The work of J. Park was partially supported by National Research Foundation of Korea under grant number NRF-2019R1A5A1028324. The authors would like to thank Ji Oon Lee for helpful discussions. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji - first_name: Jaewhi full_name: Park, Jaewhi last_name: Park citation: ama: Ji HC, Park J. Tracy-Widom limit for free sum of random matrices. The Annals of Probability. 2025;53(1):239-298. doi:10.1214/24-aop1705 apa: Ji, H. C., & Park, J. (2025). Tracy-Widom limit for free sum of random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-aop1705 chicago: Ji, Hong Chang, and Jaewhi Park. “Tracy-Widom Limit for Free Sum of Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/24-aop1705. ieee: H. C. Ji and J. Park, “Tracy-Widom limit for free sum of random matrices,” The Annals of Probability, vol. 53, no. 1. Institute of Mathematical Statistics, pp. 239–298, 2025. ista: Ji HC, Park J. 2025. Tracy-Widom limit for free sum of random matrices. The Annals of Probability. 53(1), 239–298. mla: Ji, Hong Chang, and Jaewhi Park. “Tracy-Widom Limit for Free Sum of Random Matrices.” The Annals of Probability, vol. 53, no. 1, Institute of Mathematical Statistics, 2025, pp. 239–98, doi:10.1214/24-aop1705. short: H.C. Ji, J. Park, The Annals of Probability 53 (2025) 239–298. corr_author: '1' date_created: 2025-02-17T09:32:16Z date_published: 2025-01-19T00:00:00Z date_updated: 2025-09-30T10:32:51Z day: '19' department: - _id: LaEr doi: 10.1214/24-aop1705 ec_funded: 1 external_id: arxiv: - '2110.05147' isi: - '001407834700007' intvolume: ' 53' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2110.05147 month: '01' oa: 1 oa_version: Preprint page: 239 - 298 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: issn: - 0091-1798 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Tracy-Widom limit for free sum of random matrices type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 53 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: 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: 2025-09-30T12:41:58Z day: '01' 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- OA_place: repository OA_type: green _id: '15128' abstract: - lang: eng text: We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,\zeta)$ and a general class of related quantities involving two resolvents at nearby spectral parameters. - lang: fre text: "On établit un théorème limite central universel pour les statistiques linéaires mésoscopiques des valeurs propres d’une matrice de type Wigner au milieu du spectre, avec des fonctions de classe \r\n et à support compact. La principale nouveauté de cette approche est qu’elle repose sur une loi locale optimale pour la fonction à deux points $T(z,\\zeta)$ , ainsi que pour une classe plus générale d’observables impliquant deux résolvantes évaluées en des paramètres proches." acknowledgement: "I would like to express my gratitude to László Erdős for suggesting the project and supervising my work. I am also thankful to Yuanyuan Xu and Oleksii Kolupaiev for many helpful discussions. Furthermore, I am grateful to Guillaume Dubach for translating the abstract into French.\r\nThe author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2025;61(1):129-154. doi:10.1214/23-AIHP1438 apa: Riabov, V. (2025). Mesoscopic eigenvalue statistics for Wigner-type matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AIHP1438 chicago: Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/23-AIHP1438. ieee: V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 61, no. 1. Institute of Mathematical Statistics, pp. 129–154, 2025. ista: Riabov V. 2025. Mesoscopic eigenvalue statistics for Wigner-type matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 61(1), 129–154. mla: Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 61, no. 1, Institute of Mathematical Statistics, 2025, pp. 129–54, doi:10.1214/23-AIHP1438. short: V. Riabov, Annales de l’institut Henri Poincare (B) Probability and Statistics 61 (2025) 129–154. corr_author: '1' date_created: 2024-03-20T09:41:04Z date_published: 2025-02-01T00:00:00Z date_updated: 2025-05-19T13:54:31Z day: '01' department: - _id: GradSch - _id: LaEr doi: 10.1214/23-AIHP1438 ec_funded: 1 external_id: arxiv: - '2301.01712' isi: - '001427953600004' intvolume: ' 61' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2301.01712 month: '02' oa: 1 oa_version: Preprint page: 129-154 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Annales de l'institut Henri Poincare (B) Probability and Statistics publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Mesoscopic eigenvalue statistics for Wigner-type matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 61 year: '2025' ... --- 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 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: 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' ... --- OA_place: publisher _id: '20575' abstract: - lang: eng text: "This thesis deals with eigenvalue and eigenvector universality results for random matrix ensembles equipped with non-trivial spatial structure. We consider both mean-field models with a general variance profile (Wigner-type matrices) and correlation structure (correlated matrices) among the entries, as well as non-mean-field random band matrices with bandwidth W >> N^(1/2).\r\n\r\nTo extract the universal properties of random matrix spectra and eigenvectors, we obtain concentration estimates for their resolvent, the local laws, which generalize the celebrated Wigner semicircle law for a broad class of random matrices to much finer spectral scales. The local laws hold for both a single resolvent as well as for products of multiple resolvents, known as resolvent chains, and express the remarkable approximately-deterministic behavior of these objects down to the microscopic scale.\r\n\r\nOur primary tool for establishing the local laws is the dynamical Zigzag strategy, which we develop in the setting of spatially-inhomogeneous random matrices. Our proof method systematically addresses the challenges arising from non-trivial spatial structures and is robust to all types of singularities in the spectrum, as we demonstrate in the correlated setting. Furthermore, we incorporate the analysis of the deterministic resolvent chain approximations into the dynamical framework of the Zigzag strategy, synthesizing a unified toolkit for establishing multi-resolvent local laws.\r\n\r\nUsing these methods, we prove complete eigenvector delocalization, the Eigenstate Thermalization Hypothesis, and Wigner-Dyson universality in the bulk for random band matrices down to the optimal bandwidth W >> N^(1/2). For mean-field ensembles, we establish universality of local eigenvalue statistics at the cups for random matrices with correlated entries, and the Eigenstate Thermalization Hypothesis for Wigner-type matrices in the bulk of the spectrum.\r\n\r\nFinally, this thesis also contains other applications of the multi-resolvent local laws to spatially-inhomogeneous random matrices, obtained prior to the development of the Zigzag strategy. In particular, we provide a complete analysis of mesoscopic linear-eigenvalue statistics of Wigner-type matrices in all spectral regimes, including the novel cusps, and rigorously establish the prethermalization phenomenon for deformed Wigner matrices.\r\n\r\nThe main body of this thesis consists of seven research papers (listed on page xi), each presented in a separate chapter with its own introduction and all relevant context, suitable to be read independently. We ask the reader’s indulgence for the repetitions in the historical overviews and other minor redundancies that remain among the chapters as a result. The overall Introduction, preceding the chapters, provides a condensed, informal summary of the main ideas and concepts at the core of these works.\r\n" acknowledgement: "The work comprising this thesis was supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo.101020331 awarded to my advisor." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Riabov V. Universality in random matrices with spatial structure. 2025. doi:10.15479/AT-ISTA-20575 apa: Riabov, V. (2025). Universality in random matrices with spatial structure. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-20575 chicago: Riabov, Volodymyr. “Universality in Random Matrices with Spatial Structure.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20575. ieee: V. Riabov, “Universality in random matrices with spatial structure,” Institute of Science and Technology Austria, 2025. ista: Riabov V. 2025. Universality in random matrices with spatial structure. Institute of Science and Technology Austria. mla: Riabov, Volodymyr. Universality in Random Matrices with Spatial Structure. Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-20575. short: V. Riabov, Universality in Random Matrices with Spatial Structure, Institute of Science and Technology Austria, 2025. corr_author: '1' date_created: 2025-10-29T19:12:24Z date_published: 2025-11-03T00:00:00Z date_updated: 2026-04-07T12:32:20Z day: '3' ddc: - '515' - '519' degree_awarded: PhD department: - _id: GradSch - _id: LaEr doi: 10.15479/AT-ISTA-20575 ec_funded: 1 file: - access_level: open_access checksum: 6a0487b2b66bb35d44b394756d44b8b4 content_type: application/pdf creator: vriabov date_created: 2025-10-29T18:53:59Z date_updated: 2025-10-29T18:53:59Z file_id: '20577' file_name: riabov_thesis-pdfa.pdf file_size: 7536583 relation: main_file success: 1 - access_level: closed checksum: 224efda6bf9864d296a1e5e0124c1e8f content_type: application/x-zip-compressed creator: vriabov date_created: 2025-10-29T18:54:53Z date_updated: 2025-10-29T18:54:53Z file_id: '20578' file_name: manuscript.zip file_size: 17841612 relation: source_file file_date_updated: 2025-10-29T18:54:53Z has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: '436' project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication_identifier: isbn: - 978-3-99078-064-0 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '20322' relation: part_of_dissertation status: public - id: '18764' relation: part_of_dissertation status: public - id: '13317' relation: part_of_dissertation status: public - id: '19368' relation: part_of_dissertation status: deleted - id: '18554' relation: part_of_dissertation status: public - id: '20576' relation: part_of_dissertation status: public - id: '17174' relation: part_of_dissertation status: public - id: '19547' relation: part_of_dissertation status: public - id: '19598' relation: part_of_dissertation status: public status: public supervisor: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 title: Universality in random matrices with spatial structure 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: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '19598' abstract: - lang: eng text: We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes. acknowledgement: I would like to express my gratitude to László Erdős for his careful guidance and supervision of my work. I am also thankful to Jana Reker and Joscha Henheik for many helpful discussions. 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: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Riabov V. Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. 2025;193:1183-1237. doi:10.1007/s00440-025-01373-w apa: Riabov, V. (2025). Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01373-w chicago: Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” Probability Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01373-w. ieee: V. Riabov, “Linear Eigenvalue statistics at the cusp,” Probability Theory and Related Fields, vol. 193. Springer Nature, pp. 1183–1237, 2025. ista: Riabov V. 2025. Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. 193, 1183–1237. mla: Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” Probability Theory and Related Fields, vol. 193, Springer Nature, 2025, pp. 1183–237, doi:10.1007/s00440-025-01373-w. short: V. Riabov, Probability Theory and Related Fields 193 (2025) 1183–1237. corr_author: '1' date_created: 2025-04-20T22:01:28Z date_published: 2025-12-01T00:00:00Z date_updated: 2026-04-07T12:32:19Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00440-025-01373-w external_id: arxiv: - '2307.07432' isi: - '001466997300001' file: - access_level: open_access checksum: 700229b280725c0d6aad0d71362cce5f content_type: application/pdf creator: dernst date_created: 2025-12-30T13:10:05Z date_updated: 2025-12-30T13:10:05Z file_id: '20916' file_name: 2025_ProbTheoryRelatFields_Riabov.pdf file_size: 919213 relation: main_file success: 1 file_date_updated: 2025-12-30T13:10:05Z has_accepted_license: '1' intvolume: ' 193' isi: 1 language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 1183-1237 publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 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: Linear Eigenvalue statistics at the cusp 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: 193 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18112' abstract: - lang: eng text: 'It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus.' acknowledgement: I am very grateful to Vadim Kaloshin for suggesting the topic, his guidance during this project, and many helpful comments on an earlier version of the manuscript. Moreover, I would like to thank Comlan Edmond Koudjinan and Volodymyr Riabov for interesting discussions. Partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331 is gratefully acknowledged. This project received funding from the European Research Council (ERC) ERC Grant No. 885707. article_processing_charge: Yes (via OA deal) article_type: original author: - 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: Henheik SJ. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 2025;45(2):467-503. doi:10.1017/etds.2024.48 apa: Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2024.48 chicago: Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2025. https://doi.org/10.1017/etds.2024.48. ieee: S. J. Henheik, “Deformational rigidity of integrable metrics on the torus,” Ergodic Theory and Dynamical Systems, vol. 45, no. 2. Cambridge University Press, pp. 467–503, 2025. ista: Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 45(2), 467–503. mla: Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” Ergodic Theory and Dynamical Systems, vol. 45, no. 2, Cambridge University Press, 2025, pp. 467–503, doi:10.1017/etds.2024.48. short: S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503. corr_author: '1' date_created: 2024-09-22T22:01:43Z date_published: 2025-02-01T00:00:00Z date_updated: 2026-04-07T12:37:10Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1017/etds.2024.48 ec_funded: 1 external_id: isi: - '001308182000001' file: - access_level: open_access checksum: 650fe115d998fe0ac3a8d0c7519447c8 content_type: application/pdf creator: dernst date_created: 2025-01-13T08:51:40Z date_updated: 2025-01-13T08:51:40Z file_id: '18828' file_name: 2025_ErgodicTheory_Henheik.pdf file_size: 659100 relation: main_file success: 1 file_date_updated: 2025-01-13T08:51:40Z has_accepted_license: '1' intvolume: ' 45' isi: 1 issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 467-503 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Ergodic Theory and Dynamical Systems publication_identifier: eissn: - 1469-4417 issn: - 0143-3857 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Deformational rigidity of integrable metrics on the torus 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: 45 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' ... --- 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: repository _id: '19552' abstract: - lang: eng text: "Particle creation terms in quantum Hamiltonians are usually ultraviolet\r\ndivergent and thus mathematically ill defined. A rather novel way of solving\r\nthis problem is based on imposing so-called interior-boundary conditions on the\r\nwave function. Previous papers showed that this approach works in the\r\nnon-relativistic regime, but particle creation is mostly relevant in the\r\nrelativistic case after all. In flat relativistic space-time (that is,\r\nneglecting gravity), the approach was previously found to work only for certain\r\nsomewhat artificial cases. Here, as a way of taking gravity into account, we\r\nconsider curved space-time, specifically the super-critical\r\nReissner-Nordstr\\\"om space-time, which features a naked timelike singularity.\r\nWe find that the interior-boundary approach works fully in this setting; in\r\nparticular, we prove rigorously the existence of well-defined, self-adjoint\r\nHamiltonians with particle creation at the singularity, based on\r\ninterior-boundary conditions. We also non-rigorously analyze the asymptotic\r\nbehavior of the Bohmian trajectories and construct the corresponding Bohm-Bell\r\nprocess of particle creation, motion, and annihilation. The upshot is that in\r\nquantum physics, a naked space-time singularity need not lead to a breakdown of\r\nphysical laws, but on the contrary allows for boundary conditions governing\r\nwhat comes out of the singularity and thereby removing the ultraviolet\r\ndivergence." acknowledgement: "JH gratefully acknowledges partial financial support by the ERC Advanced\r\nGrant “RMTBeyond” No. 101020331." article_processing_charge: No arxiv: 1 author: - 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: Bipul full_name: Poudyal, Bipul last_name: Poudyal - first_name: Roderich full_name: Tumulka, Roderich last_name: Tumulka citation: ama: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv. doi:10.48550/arXiv.2409.00677 apa: Henheik, S. J., Poudyal, B., & Tumulka, R. (n.d.). How a space-time singularity helps remove the ultraviolet divergence problem. arXiv. https://doi.org/10.48550/arXiv.2409.00677 chicago: Henheik, Sven Joscha, Bipul Poudyal, and Roderich Tumulka. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.00677. ieee: S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps remove the ultraviolet divergence problem,” arXiv. . ista: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv, 10.48550/arXiv.2409.00677. mla: Henheik, Sven Joscha, et al. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, doi:10.48550/arXiv.2409.00677. short: S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T12:07:25Z date_published: 2025-02-28T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '28' department: - _id: LaEr doi: 10.48550/arXiv.2409.00677 ec_funded: 1 external_id: arxiv: - '2409.00677' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2409.00677 month: '02' 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: How a space-time singularity helps remove the ultraviolet divergence problem type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 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 _id: '19540' abstract: - lang: eng text: "This thesis deals with several different models for complex quantum mechanical systems and is structured in three main parts. \r\n\t\r\nIn Part I, we study mean field random matrices as models for quantum Hamiltonians. Our focus lies on proving concentration estimates for resolvents of random matrices, so-called local laws, mostly in the setting of multiple resolvents. These estimates have profound consequences for eigenvector overlaps and thermalization problems. More concretely, we obtain, e.g., the optimal eigenstate thermalization hypothesis (ETH) uniformly in the spectrum for Wigner matrices, an optimal lower bound on non-Hermitian eigenvector overlaps, and prethermalization for deformed Wigner matrices.\tIn order to prove our novel multi-resolvent local laws, we develop and devise two main methods, the static Psi-method and the dynamical Zigzag strategy. \r\n\t\r\nIn Part II, we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic theory of superconductivity. We focus on asymptotic formulas for the characteristic critical temperature and energy gap of a superconductor and prove universality of their ratio in various physical regimes. Additionally, we investigate multi-band superconductors and show that inter-band coupling effects can only enhance the critical temperature. \r\n\t\r\nIn Part III, we study quantum lattice systems. On the one hand, we show a strong version of the local-perturbations-perturb-locally (LPPL) principle for the ground state of weakly interacting quantum spin systems with a uniform on-site gap. On the other hand, we introduce a notion of a local gap and rigorously justify response theory and the Kubo formula under the weakened assumption of a local gap. \r\n\t\r\nAdditionally, we discuss two classes of problems which do not fit into the three main parts of the thesis. These are deformational rigidity of Liouville metrics on the torus and relativistic toy models of particle creation via interior-boundary-conditions (IBCs). " alternative_title: - ISTA Thesis article_processing_charge: No author: - 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: 'Henheik SJ. Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems. 2025. doi:10.15479/AT-ISTA-19540' apa: 'Henheik, S. J. (2025). Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-19540' chicago: 'Henheik, Sven Joscha. “Modeling Complex Quantum Systems : Random Matrices, BCS Theory, and Quantum Lattice Systems.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-19540.' ieee: 'S. J. Henheik, “Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems,” Institute of Science and Technology Austria, 2025.' ista: 'Henheik SJ. 2025. Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria.' mla: 'Henheik, Sven Joscha. Modeling Complex Quantum Systems : Random Matrices, BCS Theory, and Quantum Lattice Systems. Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-19540.' short: 'S.J. Henheik, Modeling Complex Quantum Systems : Random Matrices, BCS Theory, and Quantum Lattice Systems, Institute of Science and Technology Austria, 2025.' corr_author: '1' date_created: 2025-04-10T21:21:18Z date_published: 2025-04-10T00:00:00Z date_updated: 2026-04-07T12:37:12Z day: '10' ddc: - '519' degree_awarded: PhD department: - _id: GradSch - _id: LaEr doi: 10.15479/AT-ISTA-19540 ec_funded: 1 file: - access_level: closed checksum: b8477ae5578436c72c3bb4193ad34ac5 content_type: application/zip creator: shenheik date_created: 2025-04-10T21:14:18Z date_updated: 2025-04-10T21:14:18Z file_id: '19542' file_name: Henheik-Thesis_source_final.zip file_size: 4107587 relation: source_file - access_level: open_access checksum: e9fc0ea12ec46c9f71110c33217c4140 content_type: application/pdf creator: shenheik date_created: 2025-04-11T13:16:05Z date_updated: 2025-04-11T13:16:05Z file_id: '19553' file_name: Henheik-Thesis-pdfa_FINAL.pdf file_size: 9999492 relation: main_file success: 1 - access_level: closed checksum: f94580f86c785e7108eb116cd189e225 content_type: application/pdf creator: cchlebak date_created: 2025-04-23T14:10:27Z date_updated: 2025-04-23T14:10:27Z file_id: '19615' file_name: Henheik-Thesis-Volume1_print.pdf file_size: 13276442 relation: other - access_level: closed checksum: b927ead3c78020ffb32918911deedb74 content_type: application/pdf creator: cchlebak date_created: 2025-04-23T14:11:05Z date_updated: 2025-04-23T14:11:05Z file_id: '19616' file_name: Henheik-Thesis-Volume2_print.pdf file_size: 7628767 relation: other file_date_updated: 2025-04-23T14:11:05Z has_accepted_license: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: '720' project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication_identifier: isbn: - 978-3-99078-057-2 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '14343' relation: part_of_dissertation status: public - id: '18656' relation: part_of_dissertation status: public - id: '13317' relation: part_of_dissertation status: public - id: '11732' relation: part_of_dissertation status: public - id: '12184' relation: part_of_dissertation status: public - id: '14421' relation: part_of_dissertation status: public - id: '10623' relation: part_of_dissertation status: public - id: '18112' relation: part_of_dissertation status: public - id: '19001' relation: part_of_dissertation status: public - id: '10642' relation: part_of_dissertation status: public - id: '19545' relation: part_of_dissertation status: public - id: '19546' relation: part_of_dissertation status: public - id: '19550' relation: part_of_dissertation status: public - id: '19551' relation: part_of_dissertation status: public - id: '19552' relation: part_of_dissertation status: public - id: '14542' relation: part_of_dissertation status: public - id: '17049' relation: part_of_dissertation status: public - id: '18764' relation: part_of_dissertation status: public - id: '19547' relation: part_of_dissertation status: public - id: '19548' relation: part_of_dissertation status: public status: public supervisor: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 title: 'Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems' 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: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2025' ...