--- _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 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. date_created: 2024-02-25T23:00:56Z date_published: 2024-02-01T00:00:00Z date_updated: 2024-02-27T08:29:05Z day: '01' department: - _id: LaEr doi: 10.1214/23-AAP2000 ec_funded: 1 external_id: arxiv: - '2208.12206' intvolume: ' 34' 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 34 year: '2024' ... --- _id: '11741' abstract: - lang: eng text: Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble. acknowledgement: "The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." 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: 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, Schröder DJ. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 2023;185:1183–1218. doi:10.1007/s00440-022-01156-7 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-022-01156-7 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer Nature, 2023. https://doi.org/10.1007/s00440-022-01156-7. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” Probability Theory and Related Fields, vol. 185. Springer Nature, pp. 1183–1218, 2023. ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218. mla: Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” Probability Theory and Related Fields, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:10.1007/s00440-022-01156-7. short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218. date_created: 2022-08-07T22:02:00Z date_published: 2023-04-01T00:00:00Z date_updated: 2023-08-14T12:48:09Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00440-022-01156-7 external_id: arxiv: - '2106.10200' isi: - '000830344500001' file: - access_level: open_access checksum: b9247827dae5544d1d19c37abe547abc content_type: application/pdf creator: dernst date_created: 2023-08-14T12:47:32Z date_updated: 2023-08-14T12:47:32Z file_id: '14054' file_name: 2023_ProbabilityTheory_Cipolloni.pdf file_size: 782278 relation: main_file success: 1 file_date_updated: 2023-08-14T12:47:32Z has_accepted_license: '1' intvolume: ' 185' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 1183–1218 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: Quenched universality 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: 185 year: '2023' ... --- _id: '10405' abstract: - lang: eng text: 'We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. ' acknowledgement: L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation. 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: 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, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 2023;76(5):946-1034. doi:10.1002/cpa.22028 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22028 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics. Wiley, 2023. https://doi.org/10.1002/cpa.22028. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023. ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034. mla: Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:10.1002/cpa.22028. short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034. date_created: 2021-12-05T23:01:41Z date_published: 2023-05-01T00:00:00Z date_updated: 2023-10-04T09:22:55Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1002/cpa.22028 ec_funded: 1 external_id: arxiv: - '1912.04100' isi: - '000724652500001' file: - access_level: open_access checksum: 8346bc2642afb4ccb7f38979f41df5d9 content_type: application/pdf creator: dernst date_created: 2023-10-04T09:21:48Z date_updated: 2023-10-04T09:21:48Z file_id: '14388' file_name: 2023_CommPureMathematics_Cipolloni.pdf file_size: 803440 relation: main_file success: 1 file_date_updated: 2023-10-04T09:21:48Z has_accepted_license: '1' intvolume: ' 76' isi: 1 issue: '5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 946-1034 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program 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: Central limit theorem for linear eigenvalue statistics 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 76 year: '2023' ... --- _id: '12707' abstract: - lang: eng text: We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail. article_processing_charge: No 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: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu orcid: 0000-0003-1559-1205 citation: ama: Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 2023;29(2):1063-1079. doi:10.3150/22-BEJ1490 apa: Erdös, L., & Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/22-BEJ1490 chicago: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2023. https://doi.org/10.3150/22-BEJ1490. ieee: L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” Bernoulli, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023. ista: Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079. mla: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” Bernoulli, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:10.3150/22-BEJ1490. short: L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079. date_created: 2023-03-05T23:01:05Z date_published: 2023-05-01T00:00:00Z date_updated: 2023-10-04T10:21:07Z day: '01' department: - _id: LaEr doi: 10.3150/22-BEJ1490 ec_funded: 1 external_id: arxiv: - '2112.12093 ' isi: - '000947270100008' intvolume: ' 29' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2112.12093 month: '05' oa: 1 oa_version: Preprint page: 1063-1079 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Bernoulli publication_identifier: issn: - 1350-7265 publication_status: published publisher: Bernoulli Society for Mathematical Statistics and Probability quality_controlled: '1' scopus_import: '1' status: public title: Small deviation estimates for the largest eigenvalue of Wigner matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 29 year: '2023' ... --- _id: '12792' abstract: - lang: eng text: In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics. acknowledgement: "We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation." 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: 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, Schröder DJ. On the spectral form factor for random matrices. Communications in Mathematical Physics. 2023;401:1665-1700. doi:10.1007/s00220-023-04692-y apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). On the spectral form factor for random matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04692-y chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04692-y. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” Communications in Mathematical Physics, vol. 401. Springer Nature, pp. 1665–1700, 2023. ista: Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700. mla: Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” Communications in Mathematical Physics, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:10.1007/s00220-023-04692-y. short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700. date_created: 2023-04-02T22:01:11Z date_published: 2023-07-01T00:00:00Z date_updated: 2023-10-04T12:10:31Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-023-04692-y ec_funded: 1 external_id: isi: - '000957343500001' file: - access_level: open_access checksum: 72057940f76654050ca84a221f21786c content_type: application/pdf creator: dernst date_created: 2023-10-04T12:09:18Z date_updated: 2023-10-04T12:09:18Z file_id: '14397' file_name: 2023_CommMathPhysics_Cipolloni.pdf file_size: 859967 relation: main_file success: 1 file_date_updated: 2023-10-04T12:09:18Z has_accepted_license: '1' intvolume: ' 401' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 1665-1700 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the spectral form factor 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: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 401 year: '2023' ... --- _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. 2023. doi:10.1007/s00440-023-01229-1 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). 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, 2023. 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. Springer Nature, 2023. ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. mla: Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2023, doi:10.1007/s00440-023-01229-1. short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2023). date_created: 2023-10-08T22:01:17Z date_published: 2023-09-28T00:00:00Z date_updated: 2023-10-09T07:19:01Z day: '28' department: - _id: LaEr doi: 10.1007/s00440-023-01229-1 external_id: arxiv: - '2210.12060' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2210.12060 month: '09' oa: 1 oa_version: Preprint 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: Mesoscopic central limit theorem for non-Hermitian random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '12683' abstract: - lang: eng text: We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices. acknowledgement: G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No article_type: original author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 2023;28:1-13. doi:10.1214/23-ECP516 apa: Dubach, G., & Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP516 chicago: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP516. ieee: G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023. ista: Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13. mla: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:10.1214/23-ECP516. short: G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13. date_created: 2023-02-26T23:01:01Z date_published: 2023-02-08T00:00:00Z date_updated: 2023-10-17T12:48:10Z day: '08' ddc: - '510' department: - _id: LaEr doi: 10.1214/23-ECP516 ec_funded: 1 external_id: arxiv: - '2108.13694' isi: - '000950650200005' file: - access_level: open_access checksum: a1c6f0a3e33688fd71309c86a9aad86e content_type: application/pdf creator: dernst date_created: 2023-02-27T09:43:27Z date_updated: 2023-02-27T09:43:27Z file_id: '12692' file_name: 2023_ElectCommProbability_Dubach.pdf file_size: 479105 relation: main_file success: 1 file_date_updated: 2023-02-27T09:43:27Z has_accepted_license: '1' intvolume: ' 28' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 1-13 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Electronic Communications in Probability publication_identifier: eissn: - 1083-589X publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Dynamics of a rank-one perturbation of a Hermitian matrix 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: 28 year: '2023' ... --- _id: '12761' abstract: - lang: eng text: "We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048)." acknowledgement: The second author is partially funded by the ERC Advanced Grant “RMTBEYOND” No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. article_processing_charge: No 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: 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, Schröder DJ. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 2023;33(1):447-489. doi:10.1214/22-AAP1820 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AAP1820 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AAP1820. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023. ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489. mla: Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:10.1214/22-AAP1820. short: G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489. date_created: 2023-03-26T22:01:08Z date_published: 2023-02-01T00:00:00Z date_updated: 2023-10-17T12:48:52Z day: '01' department: - _id: LaEr doi: 10.1214/22-AAP1820 ec_funded: 1 external_id: arxiv: - '2012.13218' isi: - '000946432400015' intvolume: ' 33' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2012.13218 month: '02' oa: 1 oa_version: Preprint page: 447-489 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: Functional central limit theorems for Wigner matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2023' ... --- _id: '14542' abstract: - lang: eng text: "It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit." acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427. article_number: '2360005 ' article_processing_charge: Yes (in subscription journal) 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 - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 citation: ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2023. doi:10.1142/s0129055x2360005x apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2023). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2023. https://doi.org/10.1142/s0129055x2360005x. ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics. World Scientific Publishing, 2023. ista: Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005. mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, 2360005, World Scientific Publishing, 2023, doi:10.1142/s0129055x2360005x. short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023). date_created: 2023-11-15T23:48:14Z date_published: 2023-10-31T00:00:00Z date_updated: 2023-11-20T10:04:38Z day: '31' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1142/s0129055x2360005x ec_funded: 1 external_id: arxiv: - '2301.05621' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1142/S0129055X2360005X month: '10' 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 - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: epub_ahead publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Universality in low-dimensional BCS theory 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 year: '2023' ... --- _id: '14667' abstract: - lang: eng text: 'For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. ' - lang: fre text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite. acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated editor for carefully reading this paper and providing helpful comments that improved the quality of the article. Also the authors would like to thank Peter Forrester for pointing out the reference [12] that was absent in the previous version of the manuscript." article_processing_charge: No 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: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji citation: ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105. doi:10.1214/22-AIHP1304 apa: Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304 chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304. ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023. ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105. mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304. short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105. date_created: 2023-12-10T23:01:00Z date_published: 2023-11-01T00:00:00Z date_updated: 2023-12-11T12:36:56Z day: '01' department: - _id: LaEr doi: 10.1214/22-AIHP1304 ec_funded: 1 external_id: arxiv: - '2112.11382' intvolume: ' 59' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2112.11382 month: '11' oa: 1 oa_version: Preprint page: 2083-2105 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: Functional CLT for non-Hermitian random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 59 year: '2023' ... --- _id: '13317' abstract: - lang: eng text: We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction. acknowledgement: "LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond” No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The University of Tokyo." article_number: '128' article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Shoki full_name: Sugimoto, Shoki last_name: Sugimoto - 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 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 2023;190(7). doi:10.1007/s10955-023-03132-4 apa: Sugimoto, S., Henheik, S. J., Riabov, V., & Erdös, L. (2023). Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-023-03132-4 chicago: Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” Journal of Statistical Physics. Springer Nature, 2023. https://doi.org/10.1007/s10955-023-03132-4. ieee: S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” Journal of Statistical Physics, vol. 190, no. 7. Springer Nature, 2023. ista: Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128. mla: Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” Journal of Statistical Physics, vol. 190, no. 7, 128, Springer Nature, 2023, doi:10.1007/s10955-023-03132-4. short: S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023). date_created: 2023-07-30T22:01:02Z date_published: 2023-07-21T00:00:00Z date_updated: 2023-12-13T11:38:44Z day: '21' ddc: - '510' - '530' department: - _id: LaEr doi: 10.1007/s10955-023-03132-4 ec_funded: 1 external_id: arxiv: - '2304.04213' isi: - '001035677200002' file: - access_level: open_access checksum: c2ef6b2aecfee1ad6d03fab620507c2c content_type: application/pdf creator: dernst date_created: 2023-07-31T07:49:31Z date_updated: 2023-07-31T07:49:31Z file_id: '13325' file_name: 2023_JourStatPhysics_Sugimoto.pdf file_size: 612755 relation: main_file success: 1 file_date_updated: 2023-07-31T07:49:31Z has_accepted_license: '1' intvolume: ' 190' isi: 1 issue: '7' language: - iso: eng month: '07' 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 Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Eigenstate thermalisation hypothesis for translation invariant spin 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: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 190 year: '2023' ... --- _id: '13975' abstract: - lang: eng text: "We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure." acknowledgement: "The first author thanks Yizhe Zhu for pointing out reference [30]. We thank David Renfrew for comments on an earlier draft. We thank the anonymous referee for a careful reading and helpful comments.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Andrew J full_name: Campbell, Andrew J id: 582b06a9-1f1c-11ee-b076-82ffce00dde4 last_name: Campbell - first_name: Sean full_name: O’Rourke, Sean last_name: O’Rourke citation: ama: Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 2023. doi:10.1007/s10959-023-01275-4 apa: Campbell, A. J., & O’Rourke, S. (2023). Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. Springer Nature. https://doi.org/10.1007/s10959-023-01275-4 chicago: Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability. Springer Nature, 2023. https://doi.org/10.1007/s10959-023-01275-4. ieee: A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” Journal of Theoretical Probability. Springer Nature, 2023. ista: Campbell AJ, O’Rourke S. 2023. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. mla: Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability, Springer Nature, 2023, doi:10.1007/s10959-023-01275-4. short: A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability (2023). date_created: 2023-08-06T22:01:13Z date_published: 2023-07-26T00:00:00Z date_updated: 2023-12-13T12:00:50Z day: '26' ddc: - '510' department: - _id: LaEr doi: 10.1007/s10959-023-01275-4 external_id: arxiv: - '2210.07927' isi: - '001038341000001' has_accepted_license: '1' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s10959-023-01275-4 month: '07' oa: 1 oa_version: Published Version publication: Journal of Theoretical Probability publication_identifier: eissn: - 1572-9230 issn: - 0894-9840 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Spectrum of Lévy–Khintchine random laplacian 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 year: '2023' ... --- _id: '14343' abstract: - lang: eng text: The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation. acknowledgement: "G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331." article_number: e74 article_processing_charge: Yes 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: Oleksii full_name: Kolupaiev, Oleksii id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61 last_name: Kolupaiev citation: ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.70 apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.70 chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.70. ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023. ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74. mla: Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 11, e74, Cambridge University Press, 2023, doi:10.1017/fms.2023.70. short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023). date_created: 2023-09-17T22:01:09Z date_published: 2023-08-23T00:00:00Z date_updated: 2023-12-13T12:24:23Z day: '23' ddc: - '510' department: - _id: LaEr - _id: GradSch doi: 10.1017/fms.2023.70 ec_funded: 1 external_id: arxiv: - '2301.05181' isi: - '001051980200001' file: - access_level: open_access checksum: eb747420e6a88a7796fa934151957676 content_type: application/pdf creator: dernst date_created: 2023-09-20T11:09:35Z date_updated: 2023-09-20T11:09:35Z file_id: '14352' file_name: 2023_ForumMathematics_Cipolloni.pdf file_size: 852652 relation: main_file success: 1 file_date_updated: 2023-09-20T11:09:35Z has_accepted_license: '1' intvolume: ' 11' isi: 1 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: Forum of Mathematics, Sigma publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Gaussian fluctuations in the equipartition principle 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: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '14421' abstract: - lang: eng text: Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\in\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\psi_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission). acknowledgement: J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331. article_number: '445201' 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 - first_name: Roderich full_name: Tumulka, Roderich last_name: Tumulka citation: ama: 'Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 2023;56(44). doi:10.1088/1751-8121/acfe62' apa: 'Henheik, S. J., & Tumulka, R. (2023). Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/acfe62' chicago: 'Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2023. https://doi.org/10.1088/1751-8121/acfe62.' ieee: 'S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point source,” Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 44. IOP Publishing, 2023.' ista: 'Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201.' mla: 'Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:10.1088/1751-8121/acfe62.' short: 'S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical 56 (2023).' date_created: 2023-10-12T12:42:53Z date_published: 2023-10-11T00:00:00Z date_updated: 2023-12-13T13:01:25Z day: '11' ddc: - '510' department: - _id: GradSch - _id: LaEr doi: 10.1088/1751-8121/acfe62 ec_funded: 1 external_id: arxiv: - '2211.16606' isi: - '001080908000001' file: - access_level: open_access checksum: 5b68de147dd4c608b71a6e0e844d2ce9 content_type: application/pdf creator: dernst date_created: 2023-10-16T07:07:24Z date_updated: 2023-10-16T07:07:24Z file_id: '14429' file_name: 2023_JourPhysics_Henheik.pdf file_size: 721399 relation: main_file success: 1 file_date_updated: 2023-10-16T07:07:24Z has_accepted_license: '1' intvolume: ' 56' isi: 1 issue: '44' language: - iso: eng month: '10' 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 Physics A: Mathematical and Theoretical' publication_identifier: eissn: - 1751-8121 issn: - 1751-8113 publication_status: published publisher: IOP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Creation rate of Dirac particles at a point source 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: 56 year: '2023' ... --- _id: '14750' abstract: - lang: eng text: "Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \x02 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \x02μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. " acknowledgement: "The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments." article_processing_charge: No article_type: original author: - first_name: Xiucai full_name: Ding, Xiucai last_name: Ding - first_name: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji citation: ama: Ding X, Ji HC. Local laws for multiplication of random matrices. The Annals of Applied Probability. 2023;33(4):2981-3009. doi:10.1214/22-aap1882 apa: Ding, X., & Ji, H. C. (2023). Local laws for multiplication of random matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1882 chicago: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1882. ieee: X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” The Annals of Applied Probability, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023. ista: Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009. mla: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:10.1214/22-aap1882. short: X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009. date_created: 2024-01-08T13:03:18Z date_published: 2023-08-01T00:00:00Z date_updated: 2024-01-09T08:16:41Z day: '01' department: - _id: LaEr doi: 10.1214/22-aap1882 ec_funded: 1 external_id: arxiv: - '2010.16083' intvolume: ' 33' issue: '4' keyword: - Statistics - Probability and Uncertainty - Statistics and Probability language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2010.16083 month: '08' oa: 1 oa_version: Preprint page: 2981-3009 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: The 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: Local laws for multiplication of random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2023' ... --- _id: '14775' abstract: - lang: eng text: We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble. acknowledgement: K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No article_type: original author: - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu orcid: 0000-0003-1559-1205 citation: ama: Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 2023;33(1):677-725. doi:10.1214/22-aap1826 apa: Schnelli, K., & Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1826 chicago: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1826. ieee: K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” The Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023. ista: Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725. mla: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:10.1214/22-aap1826. short: K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725. date_created: 2024-01-10T09:23:31Z date_published: 2023-02-01T00:00:00Z date_updated: 2024-01-10T13:31:46Z day: '01' department: - _id: LaEr doi: 10.1214/22-aap1826 ec_funded: 1 external_id: arxiv: - '2108.02728' isi: - '000946432400021' intvolume: ' 33' isi: 1 issue: '1' keyword: - Statistics - Probability and Uncertainty - Statistics and Probability language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2108.02728 month: '02' oa: 1 oa_version: Preprint page: 677-725 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: The 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: Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2023' ... --- _id: '14780' abstract: - lang: eng text: In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix. acknowledgement: The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Xiucai full_name: Ding, Xiucai last_name: Ding - first_name: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji citation: ama: Ding X, Ji HC. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 2023;163:25-60. doi:10.1016/j.spa.2023.05.009 apa: Ding, X., & Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2023.05.009 chicago: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications. Elsevier, 2023. https://doi.org/10.1016/j.spa.2023.05.009. ieee: X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” Stochastic Processes and their Applications, vol. 163. Elsevier, pp. 25–60, 2023. ista: Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60. mla: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications, vol. 163, Elsevier, 2023, pp. 25–60, doi:10.1016/j.spa.2023.05.009. short: X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60. date_created: 2024-01-10T09:29:25Z date_published: 2023-09-01T00:00:00Z date_updated: 2024-01-16T08:49:51Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1016/j.spa.2023.05.009 ec_funded: 1 external_id: arxiv: - '2302.13502' isi: - '001113615900001' file: - access_level: open_access checksum: 46a708b0cd5569a73d0f3d6c3e0a44dc content_type: application/pdf creator: dernst date_created: 2024-01-16T08:47:31Z date_updated: 2024-01-16T08:47:31Z file_id: '14806' file_name: 2023_StochasticProcAppl_Ding.pdf file_size: 1870349 relation: main_file success: 1 file_date_updated: 2024-01-16T08:47:31Z has_accepted_license: '1' intvolume: ' 163' isi: 1 keyword: - Applied Mathematics - Modeling and Simulation - Statistics and Probability language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 25-60 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Stochastic Processes and their Applications publication_identifier: eissn: - 1879-209X issn: - 0304-4149 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: Spiked multiplicative random matrices and principal components 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: 163 year: '2023' ... --- _id: '14849' abstract: - lang: eng text: We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal. acknowledgement: "The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation." article_processing_charge: No 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: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 - first_name: Yuanyuan full_name: Xu, Yuanyuan last_name: Xu citation: ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 2023;51(6):2192-2242. doi:10.1214/23-aop1643 apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-aop1643 chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-aop1643. ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” The Annals of Probability, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023. ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242. mla: Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:10.1214/23-aop1643. short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242. date_created: 2024-01-22T08:08:41Z date_published: 2023-11-01T00:00:00Z date_updated: 2024-01-23T10:56:30Z day: '01' department: - _id: LaEr doi: 10.1214/23-aop1643 ec_funded: 1 external_id: arxiv: - '2206.04448' intvolume: ' 51' issue: '6' keyword: - Statistics - Probability and Uncertainty - Statistics and Probability language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2206.04448 month: '11' oa: 1 oa_version: Preprint page: 2192-2242 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' status: public title: On the rightmost eigenvalue of non-Hermitian random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 51 year: '2023' ... --- _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\r\nat nearby spectral parameters. " acknowledgement: Supported by the ERC Advanced Grant ”RMTBeyond” No. 101020331 article_number: '2301.01712' 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. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. doi:10.48550/arXiv.2301.01712 apa: Riabov, V. (n.d.). Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. https://doi.org/10.48550/arXiv.2301.01712 chicago: Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2301.01712. ieee: V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” arXiv. . ista: Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv, 2301.01712. mla: Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, 2301.01712, doi:10.48550/arXiv.2301.01712. short: V. Riabov, ArXiv (n.d.). date_created: 2024-03-20T09:41:04Z date_published: 2023-01-04T00:00:00Z date_updated: 2024-03-25T12:48:20Z day: '04' department: - _id: GradSch - _id: LaEr doi: 10.48550/arXiv.2301.01712 ec_funded: 1 external_id: arxiv: - '2301.01712' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2301.01712 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: submitted status: public title: Mesoscopic eigenvalue statistics for Wigner-type matrices type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '12179' abstract: - lang: eng text: We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146]. article_processing_charge: No 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: 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, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487. doi:10.1137/21m1424408 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487. mla: Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408. short: G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487. date_created: 2023-01-12T12:12:38Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-01-27T06:56:06Z day: '01' department: - _id: LaEr doi: 10.1137/21m1424408 external_id: arxiv: - '2105.13719' intvolume: ' 43' issue: '3' keyword: - Analysis language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.13719 month: '07' oa: 1 oa_version: Preprint page: 1469-1487 publication: SIAM Journal on Matrix Analysis and Applications publication_identifier: eissn: - 1095-7162 issn: - 0895-4798 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: On the condition number of the shifted real Ginibre ensemble type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 43 year: '2022' ... --- _id: '10600' abstract: - lang: eng text: We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article. acknowledgement: J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331. article_number: '011901' article_processing_charge: No 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 - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel citation: ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632' apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0051632' chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.' ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” Journal of Mathematical Physics, vol. 63, no. 1. AIP Publishing, 2022.' ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.' mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.' short: S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022). date_created: 2022-01-03T12:19:48Z date_published: 2022-01-03T00:00:00Z date_updated: 2023-08-02T13:44:32Z day: '03' department: - _id: GradSch - _id: LaEr doi: 10.1063/5.0051632 ec_funded: 1 external_id: arxiv: - '2012.15238' isi: - '000739446000009' intvolume: ' 63' isi: 1 issue: '1' keyword: - mathematical physics - statistical and nonlinear physics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2012.15238 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: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' status: public title: 'Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '10642' abstract: - lang: eng text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences. acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL. article_number: '9' article_processing_charge: No 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 - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel - first_name: Tom full_name: Wessel, Tom last_name: Wessel citation: ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y apa: Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y. ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” Letters in Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022. ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9. mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y. short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022). date_created: 2022-01-18T16:18:25Z date_published: 2022-01-18T00:00:00Z date_updated: 2023-08-02T13:57:02Z day: '18' ddc: - '530' department: - _id: GradSch - _id: LaEr doi: 10.1007/s11005-021-01494-y ec_funded: 1 external_id: arxiv: - '2106.13780' isi: - '000744930400001' file: - access_level: open_access checksum: 7e8e69b76e892c305071a4736131fe18 content_type: application/pdf creator: cchlebak date_created: 2022-01-19T09:41:14Z date_updated: 2022-01-19T09:41:14Z file_id: '10647' file_name: 2022_LettersMathPhys_Henheik.pdf file_size: 357547 relation: main_file success: 1 file_date_updated: 2022-01-19T09:41:14Z has_accepted_license: '1' intvolume: ' 112' isi: 1 issue: '1' keyword: - mathematical physics - statistical and nonlinear physics language: - iso: eng 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: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Local stability of ground states in locally gapped and weakly interacting quantum spin 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 112 year: '2022' ... --- _id: '10643' abstract: - lang: eng text: "We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n" acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged. article_number: e4 article_processing_charge: Yes 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 - first_name: Stefan full_name: Teufel, Stefan last_name: Teufel citation: ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80' apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80' chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.' ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.' ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.' mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.' short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022). date_created: 2022-01-18T16:18:51Z date_published: 2022-01-18T00:00:00Z date_updated: 2023-08-02T13:53:11Z day: '18' ddc: - '510' department: - _id: GradSch - _id: LaEr doi: 10.1017/fms.2021.80 ec_funded: 1 external_id: arxiv: - '2012.15239' isi: - '000743615000001' file: - access_level: open_access checksum: 87592a755adcef22ea590a99dc728dd3 content_type: application/pdf creator: cchlebak date_created: 2022-01-19T09:27:43Z date_updated: 2022-01-19T09:27:43Z file_id: '10646' file_name: 2022_ForumMathSigma_Henheik.pdf file_size: 705323 relation: main_file success: 1 file_date_updated: 2022-01-19T09:27:43Z has_accepted_license: '1' intvolume: ' 10' isi: 1 keyword: - computational mathematics - discrete mathematics and combinatorics - geometry and topology - mathematical physics - statistics and probability - algebra and number theory - theoretical computer science - analysis language: - iso: eng 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: Forum of Mathematics, Sigma publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' status: public title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk' 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 10 year: '2022' ... --- _id: '10623' abstract: - lang: eng text: We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory. acknowledgement: I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions. article_number: '3' 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. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0 apa: Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0 chicago: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0. ieee: S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022. ista: Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3. mla: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0. short: S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022). date_created: 2022-01-13T15:40:53Z date_published: 2022-01-11T00:00:00Z date_updated: 2023-08-02T13:51:52Z day: '11' ddc: - '514' department: - _id: GradSch - _id: LaEr doi: 10.1007/s11040-021-09415-0 ec_funded: 1 external_id: arxiv: - '2106.02015' isi: - '000741387600001' file: - access_level: open_access checksum: d44f8123a52592a75b2c3b8ee2cd2435 content_type: application/pdf creator: cchlebak date_created: 2022-01-14T07:27:45Z date_updated: 2022-01-14T07:27:45Z file_id: '10624' file_name: 2022_MathPhyAnalGeo_Henheik.pdf file_size: 505804 relation: main_file success: 1 file_date_updated: 2022-01-14T07:27:45Z has_accepted_license: '1' intvolume: ' 25' isi: 1 issue: '1' keyword: - geometry and topology - mathematical physics language: - iso: eng 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 - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Mathematical Physics, Analysis and Geometry publication_identifier: eissn: - 1572-9656 issn: - 1385-0172 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS critical temperature at high density 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 25 year: '2022' ... --- _id: '10732' abstract: - lang: eng text: We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices. acknowledgement: We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices. article_number: '109394' 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: 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, Schröder DJ. Thermalisation for Wigner matrices. Journal of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109394. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394. mla: Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis, vol. 282, no. 8, 109394, Elsevier, 2022, doi:10.1016/j.jfa.2022.109394. short: G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022). date_created: 2022-02-06T23:01:30Z date_published: 2022-04-15T00:00:00Z date_updated: 2023-08-02T14:12:35Z day: '15' ddc: - '500' department: - _id: LaEr doi: 10.1016/j.jfa.2022.109394 external_id: arxiv: - '2102.09975' isi: - '000781239100004' file: - access_level: open_access checksum: b75fdad606ab507dc61109e0907d86c0 content_type: application/pdf creator: dernst date_created: 2022-07-29T07:22:08Z date_updated: 2022-07-29T07:22:08Z file_id: '11690' file_name: 2022_JourFunctionalAnalysis_Cipolloni.pdf file_size: 652573 relation: main_file success: 1 file_date_updated: 2022-07-29T07:22:08Z has_accepted_license: '1' intvolume: ' 282' isi: 1 issue: '8' language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Thermalisation 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 282 year: '2022' ... --- _id: '11135' abstract: - lang: eng text: We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one. article_number: '2250036' article_processing_charge: No article_type: original author: - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker citation: ama: 'Reker J. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368' apa: 'Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368' chicago: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications. World Scientific, 2022. https://doi.org/10.1142/s2010326322500368.' ieee: 'J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World Scientific, 2022.' ista: 'Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.' mla: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:10.1142/s2010326322500368.' short: 'J. Reker, Random Matrices: Theory and Applications 11 (2022).' date_created: 2022-04-08T07:11:12Z date_published: 2022-10-01T00:00:00Z date_updated: 2023-08-03T06:32:22Z day: '01' department: - _id: GradSch - _id: LaEr doi: 10.1142/s2010326322500368 external_id: arxiv: - '2103.03906' isi: - '000848873800001' intvolume: ' 11' isi: 1 issue: '4' keyword: - Discrete Mathematics and Combinatorics - Statistics - Probability and Uncertainty - Statistics and Probability - Algebra and Number Theory language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2103.03906' month: '10' oa: 1 oa_version: Preprint publication: 'Random Matrices: Theory and Applications' publication_identifier: eissn: - 2010-3271 issn: - 2010-3263 publication_status: published publisher: World Scientific quality_controlled: '1' scopus_import: '1' status: public title: On the operator norm of a Hermitian random matrix with correlated entries type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 11 year: '2022' ... --- _id: '11332' abstract: - lang: eng text: We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles. acknowledgement: Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No article_type: original author: - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu citation: ama: Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 2022;393:839-907. doi:10.1007/s00220-022-04377-y apa: Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y chicago: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y. ieee: K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” Communications in Mathematical Physics, vol. 393. Springer Nature, pp. 839–907, 2022. ista: Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907. mla: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y. short: K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907. date_created: 2022-04-24T22:01:44Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-08-03T06:34:24Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-022-04377-y ec_funded: 1 external_id: arxiv: - '2102.04330' isi: - '000782737200001' file: - access_level: open_access checksum: bee0278c5efa9a33d9a2dc8d354a6c51 content_type: application/pdf creator: dernst date_created: 2022-08-05T06:01:13Z date_updated: 2022-08-05T06:01:13Z file_id: '11726' file_name: 2022_CommunMathPhys_Schnelli.pdf file_size: 1141462 relation: main_file success: 1 file_date_updated: 2022-08-05T06:01:13Z has_accepted_license: '1' intvolume: ' 393' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 839-907 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 393 year: '2022' ... --- _id: '11418' abstract: - lang: eng text: "We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048)." acknowledgement: L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions. article_processing_charge: No 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: 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, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012. mla: Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552. short: G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012. date_created: 2022-05-29T22:01:53Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-03T07:16:53Z day: '01' department: - _id: LaEr doi: 10.1214/21-AOP1552 external_id: arxiv: - '2103.06730' isi: - '000793963400005' intvolume: ' 50' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2103.06730 month: '05' oa: 1 oa_version: Preprint page: 984-1012 publication: Annals of Probability publication_identifier: eissn: - 2168-894X issn: - 0091-1798 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Normal fluctuation in quantum ergodicity for Wigner matrices type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 50 year: '2022' ... --- _id: '12110' abstract: - lang: eng text: A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential. acknowledgement: "J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n" article_number: '122302' article_processing_charge: No 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 - first_name: Roderich full_name: Tumulka, Roderich last_name: Tumulka citation: ama: Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0104675 apa: Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104675 chicago: Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104675. ieee: S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022. ista: Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302. mla: Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675. short: S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022). date_created: 2023-01-08T23:00:53Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-03T14:12:01Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1063/5.0104675 ec_funded: 1 external_id: isi: - '000900748900002' file: - access_level: open_access checksum: 5150287295e0ce4f12462c990744d65d content_type: application/pdf creator: dernst date_created: 2023-01-20T11:58:59Z date_updated: 2023-01-20T11:58:59Z file_id: '12327' file_name: 2022_JourMathPhysics_Henheik.pdf file_size: 5436804 relation: main_file success: 1 file_date_updated: 2023-01-20T11:58:59Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '12' language: - iso: eng month: '12' 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 Mathematical Physics publication_identifier: issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Interior-boundary conditions for the Dirac equation at point sources in three dimensions 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '12148' abstract: - lang: eng text: 'We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.' acknowledgement: L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. article_number: e96 article_processing_charge: No 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: 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, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96. mla: Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86. short: G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022). date_created: 2023-01-12T12:07:30Z date_published: 2022-10-27T00:00:00Z date_updated: 2023-08-04T09:00:35Z day: '27' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2022.86 ec_funded: 1 external_id: isi: - '000873719200001' file: - access_level: open_access checksum: 94a049aeb1eea5497aa097712a73c400 content_type: application/pdf creator: dernst date_created: 2023-01-24T10:02:40Z date_updated: 2023-01-24T10:02:40Z file_id: '12356' file_name: 2022_ForumMath_Cipolloni.pdf file_size: 817089 relation: main_file success: 1 file_date_updated: 2023-01-24T10:02:40Z has_accepted_license: '1' intvolume: ' 10' isi: 1 keyword: - Computational Mathematics - Discrete Mathematics and Combinatorics - Geometry and Topology - Mathematical Physics - Statistics and Probability - Algebra and Number Theory - Theoretical Computer Science - Analysis language: - iso: eng month: '10' 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: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Rank-uniform local law 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 10 year: '2022' ... --- _id: '12184' abstract: - lang: eng text: We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs. acknowledgement: "It is a pleasure to thank Stefan Teufel for numerous interesting discussions, fruitful collaboration, and many helpful comments on an earlier version of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges financial support from the DFG research unit FOR 5413 “Long-range interacting quantum spin systems out of equilibrium: Experiment, Theory and Mathematics.\" " article_number: '121101' article_processing_charge: No 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 - first_name: Tom full_name: Wessel, Tom last_name: Wessel citation: ama: Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0123441 apa: Henheik, S. J., & Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0123441 chicago: Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0123441. ieee: S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022. ista: Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101. mla: Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:10.1063/5.0123441. short: S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022). date_created: 2023-01-15T23:00:52Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-04T09:14:57Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1063/5.0123441 ec_funded: 1 external_id: arxiv: - '2208.12220' isi: - '000905776200001' file: - access_level: open_access checksum: 213b93750080460718c050e4967cfdb4 content_type: application/pdf creator: dernst date_created: 2023-01-27T07:10:52Z date_updated: 2023-01-27T07:10:52Z file_id: '12410' file_name: 2022_JourMathPhysics_Henheik2.pdf file_size: 5251092 relation: main_file success: 1 file_date_updated: 2023-01-27T07:10:52Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '12' language: - iso: eng month: '12' 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 Mathematical Physics publication_identifier: issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: On adiabatic theory for extended fermionic 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '12214' abstract: - lang: eng text: 'Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. ' acknowledgement: "Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). " article_processing_charge: No article_type: original author: - first_name: György Pál full_name: Gehér, György Pál last_name: Gehér - first_name: Tamás full_name: Titkos, Tamás last_name: Titkos - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: 'Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894. doi:10.1112/jlms.12676' apa: 'Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12676' chicago: 'Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676.' ieee: 'G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.' ista: 'Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.' mla: 'Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:10.1112/jlms.12676.' short: G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894. date_created: 2023-01-16T09:46:13Z date_published: 2022-09-18T00:00:00Z date_updated: 2023-08-04T09:24:17Z day: '18' department: - _id: LaEr doi: 10.1112/jlms.12676 ec_funded: 1 external_id: arxiv: - '2102.02037' isi: - '000854878500001' intvolume: ' 106' isi: 1 issue: '4' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2102.02037 month: '09' oa: 1 oa_version: Preprint page: 3865-3894 project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: 'The isometry group of Wasserstein spaces: The Hilbertian case' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 106 year: '2022' ... --- _id: '12232' abstract: - lang: eng text: We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold. acknowledgement: Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. article_processing_charge: No 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: 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, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002. doi:10.1007/s00023-022-01188-8 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-022-01188-8 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002. mla: Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8. short: G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002. date_created: 2023-01-16T09:50:26Z date_published: 2022-11-01T00:00:00Z date_updated: 2023-08-04T09:33:52Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00023-022-01188-8 external_id: isi: - '000796323500001' file: - access_level: open_access checksum: 5582f059feeb2f63e2eb68197a34d7dc content_type: application/pdf creator: dernst date_created: 2023-01-27T11:06:47Z date_updated: 2023-01-27T11:06:47Z file_id: '12424' file_name: 2022_AnnalesHenriP_Cipolloni.pdf file_size: 1333638 relation: main_file success: 1 file_date_updated: 2023-01-27T11:06:47Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '11' keyword: - Mathematical Physics - Nuclear and High Energy Physics - Statistical and Nonlinear Physics language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 3981-4002 publication: Annales Henri Poincaré publication_identifier: eissn: - 1424-0661 issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Density of small singular values of the shifted real Ginibre ensemble 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 23 year: '2022' ... --- _id: '12243' abstract: - lang: eng text: 'We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ' acknowledgement: "The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation." article_number: '103303' 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: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu citation: ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290 apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104290 chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290. ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022. ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303. mla: Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:10.1063/5.0104290. short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022). date_created: 2023-01-16T09:52:58Z date_published: 2022-10-14T00:00:00Z date_updated: 2023-08-04T09:40:02Z day: '14' ddc: - '510' - '530' department: - _id: LaEr doi: 10.1063/5.0104290 ec_funded: 1 external_id: arxiv: - '2206.04443' isi: - '000869715800001' file: - access_level: open_access checksum: 2db278ae5b07f345a7e3fec1f92b5c33 content_type: application/pdf creator: dernst date_created: 2023-01-30T08:01:10Z date_updated: 2023-01-30T08:01:10Z file_id: '12436' file_name: 2022_JourMathPhysics_Cipolloni2.pdf file_size: 7356807 relation: main_file success: 1 file_date_updated: 2023-01-30T08:01:10Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '10' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '10' 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 Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Directional extremal statistics for Ginibre eigenvalues 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '12290' abstract: - lang: eng text: We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale. acknowledgement: L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. article_processing_charge: No 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: 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, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022. ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38. mla: Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:10.1214/22-ejp838. short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38. date_created: 2023-01-16T10:04:38Z date_published: 2022-09-12T00:00:00Z date_updated: 2023-08-04T10:32:23Z day: '12' ddc: - '510' department: - _id: LaEr doi: 10.1214/22-ejp838 ec_funded: 1 external_id: isi: - '000910863700003' file: - access_level: open_access checksum: bb647b48fbdb59361210e425c220cdcb content_type: application/pdf creator: dernst date_created: 2023-01-30T11:59:21Z date_updated: 2023-01-30T11:59:21Z file_id: '12464' file_name: 2022_ElecJournProbability_Cipolloni.pdf file_size: 502149 relation: main_file success: 1 file_date_updated: 2023-01-30T11:59:21Z has_accepted_license: '1' intvolume: ' 27' isi: 1 keyword: - Statistics - Probability and Uncertainty - Statistics and Probability language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 1-38 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' scopus_import: '1' status: public title: Optimal multi-resolvent local laws 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 27 year: '2022' ... --- _id: '11732' abstract: - lang: eng text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. 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: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9 apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9 chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9. ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022. ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5. mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9. short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022). date_created: 2022-08-05T11:36:56Z date_published: 2022-07-29T00:00:00Z date_updated: 2023-09-05T14:57:49Z day: '29' ddc: - '530' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1007/s10955-022-02965-9 ec_funded: 1 external_id: isi: - '000833007200002' file: - access_level: open_access checksum: b398c4dbf65f71d417981d6e366427e9 content_type: application/pdf creator: dernst date_created: 2022-08-08T07:36:34Z date_updated: 2022-08-08T07:36:34Z file_id: '11746' file_name: 2022_JourStatisticalPhysics_Henheik.pdf file_size: 419563 relation: main_file success: 1 file_date_updated: 2022-08-08T07:36:34Z has_accepted_license: '1' intvolume: ' 189' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' 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 Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS energy gap at high density 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: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 189 year: '2022' ... --- _id: '10285' abstract: - lang: eng text: We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur. acknowledgement: We acknowledge partial support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would like to thank Paul Bourgade and László Erdős for many helpful comments. article_number: '124' article_processing_charge: No article_type: original author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 citation: ama: Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686 apa: Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP686 chicago: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP686. ieee: G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021. ista: Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124. mla: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP686. short: G. Dubach, Electronic Journal of Probability 26 (2021). date_created: 2021-11-14T23:01:25Z date_published: 2021-09-28T00:00:00Z date_updated: 2021-11-15T10:48:46Z day: '28' ddc: - '519' department: - _id: LaEr doi: 10.1214/21-EJP686 ec_funded: 1 file: - access_level: open_access checksum: 1c975afb31460277ce4d22b93538e5f9 content_type: application/pdf creator: cchlebak date_created: 2021-11-15T10:10:17Z date_updated: 2021-11-15T10:10:17Z file_id: '10288' file_name: 2021_ElecJournalProb_Dubach.pdf file_size: 735940 relation: main_file success: 1 file_date_updated: 2021-11-15T10:10:17Z has_accepted_license: '1' intvolume: ' 26' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Electronic Journal of Probability publication_identifier: eissn: - 1083-6489 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: On eigenvector statistics in the spherical and truncated unitary ensembles 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: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 26 year: '2021' ... --- _id: '9230' abstract: - lang: eng text: "We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals." acknowledgement: The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099. article_number: '2103.04817' article_processing_charge: No author: - first_name: Louis-Pierre full_name: Arguin, Louis-Pierre last_name: Arguin - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: Lisa full_name: Hartung, Lisa last_name: Hartung citation: ama: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817 apa: Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817 chicago: Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.04817. ieee: L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” arXiv. . ista: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817. mla: Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817. short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.). date_created: 2021-03-09T11:08:15Z date_published: 2021-03-08T00:00:00Z date_updated: 2023-05-03T10:22:59Z day: '08' department: - _id: LaEr doi: 10.48550/arXiv.2103.04817 ec_funded: 1 external_id: arxiv: - '2103.04817' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2103.04817 month: '03' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: arXiv publication_status: submitted status: public title: Maxima of a random model of the Riemann zeta function over intervals of varying length type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '9281' abstract: - lang: eng text: We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics. article_number: '2103.11389' article_processing_charge: No author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: Fabian full_name: Mühlböck, Fabian id: 6395C5F6-89DF-11E9-9C97-6BDFE5697425 last_name: Mühlböck orcid: 0000-0003-1548-0177 citation: ama: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv. doi:10.48550/arXiv.2103.11389 apa: Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389 chicago: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389. ieee: G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” arXiv. . ista: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389. mla: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389. short: G. Dubach, F. Mühlböck, ArXiv (n.d.). date_created: 2021-03-23T05:38:48Z date_published: 2021-03-21T00:00:00Z date_updated: 2023-05-03T10:26:45Z day: '21' department: - _id: LaEr - _id: ToHe doi: 10.48550/arXiv.2103.11389 ec_funded: 1 external_id: arxiv: - '2103.11389' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2103.11389 month: '03' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: arXiv publication_status: submitted related_material: record: - id: '9946' relation: other status: public status: public title: Formal verification of Zagier's one-sentence proof type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '8373' abstract: - lang: eng text: It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim. acknowledgement: "The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601." article_processing_charge: No article_type: original author: - first_name: József full_name: Pitrik, József last_name: Pitrik - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007 apa: Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007 chicago: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007. ieee: J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021. ista: Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217. mla: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021, pp. 203–17, doi:10.1016/j.laa.2020.09.007. short: J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217. date_created: 2020-09-11T08:35:50Z date_published: 2021-01-15T00:00:00Z date_updated: 2023-08-04T10:58:14Z day: '15' department: - _id: LaEr doi: 10.1016/j.laa.2020.09.007 ec_funded: 1 external_id: arxiv: - '2002.11678' isi: - '000581730500011' intvolume: ' 609' isi: 1 keyword: - Kubo-Ando mean - weighted multivariate mean - barycenter language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2002.11678 month: '01' oa: 1 oa_version: Preprint page: 203-217 project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Linear Algebra and its Applications publication_identifier: issn: - 0024-3795 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 609 year: '2021' ... --- _id: '9036' abstract: - lang: eng text: In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space. acknowledgement: D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601. article_number: '107595' article_processing_charge: No article_type: original author: - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595 apa: Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595 chicago: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595. ieee: D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021. ista: Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595. mla: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595. short: D. Virosztek, Advances in Mathematics 380 (2021). date_created: 2021-01-22T17:55:17Z date_published: 2021-03-26T00:00:00Z date_updated: 2023-08-07T13:34:48Z day: '26' department: - _id: LaEr doi: 10.1016/j.aim.2021.107595 ec_funded: 1 external_id: arxiv: - '1910.10447' isi: - '000619676100035' intvolume: ' 380' isi: 1 issue: '3' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.10447 month: '03' oa: 1 oa_version: Preprint project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: The metric property of the quantum Jensen-Shannon divergence type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 380 year: '2021' ... --- _id: '9412' abstract: - lang: eng text: We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness. article_number: '24' article_processing_charge: No 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: 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, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP591 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021. ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24. mla: Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591. short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021). date_created: 2021-05-23T22:01:44Z date_published: 2021-03-23T00:00:00Z date_updated: 2023-08-08T13:39:19Z day: '23' ddc: - '510' department: - _id: LaEr doi: 10.1214/21-EJP591 ec_funded: 1 external_id: arxiv: - '2002.02438' isi: - '000641855600001' file: - access_level: open_access checksum: 864ab003ad4cffea783f65aa8c2ba69f content_type: application/pdf creator: kschuh date_created: 2021-05-25T13:24:19Z date_updated: 2021-05-25T13:24:19Z file_id: '9423' file_name: 2021_EJP_Cipolloni.pdf file_size: 865148 relation: main_file success: 1 file_date_updated: 2021-05-25T13:24:19Z has_accepted_license: '1' intvolume: ' 26' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: Electronic Journal of Probability publication_identifier: eissn: - '10836489' publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Fluctuation around the circular law for random matrices with real 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 26 year: '2021' ... --- _id: '9550' abstract: - lang: eng text: 'We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. ' acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation article_number: e44 article_processing_charge: No article_type: original author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38 apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.38 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.38. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021. ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44. mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38. short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021). date_created: 2021-06-13T22:01:33Z date_published: 2021-05-27T00:00:00Z date_updated: 2023-08-08T14:03:40Z day: '27' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2021.38 ec_funded: 1 external_id: arxiv: - '2008.07061' isi: - '000654960800001' file: - access_level: open_access checksum: 47c986578de132200d41e6d391905519 content_type: application/pdf creator: cziletti date_created: 2021-06-15T14:40:45Z date_updated: 2021-06-15T14:40:45Z file_id: '9555' file_name: 2021_ForumMath_Bao.pdf file_size: 483458 relation: main_file success: 1 file_date_updated: 2021-06-15T14:40:45Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Equipartition principle 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ... --- _id: '9912' abstract: - lang: eng text: "In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440 channels, the density \U0001D70C of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit \U0001D719→0, we recover the formula for the density \U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any \U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries." acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks. article_processing_charge: Yes (in subscription journal) 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: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: Yuriy full_name: Nemish, Yuriy id: 4D902E6A-F248-11E8-B48F-1D18A9856A87 last_name: Nemish orcid: 0000-0002-7327-856X citation: ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6 apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . Springer Nature. https://doi.org/10.1007/s00023-021-01085-6 chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6. ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature, pp. 4205–4269, 2021. ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269. mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:10.1007/s00023-021-01085-6. short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269. date_created: 2021-08-15T22:01:29Z date_published: 2021-12-01T00:00:00Z date_updated: 2023-08-11T10:31:48Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00023-021-01085-6 ec_funded: 1 external_id: arxiv: - '1911.05112' isi: - '000681531500001' file: - access_level: open_access checksum: 8d6bac0e2b0a28539608b0538a8e3b38 content_type: application/pdf creator: dernst date_created: 2022-05-12T12:50:27Z date_updated: 2022-05-12T12:50:27Z file_id: '11365' file_name: 2021_AnnHenriPoincare_Erdoes.pdf file_size: 1162454 relation: main_file success: 1 file_date_updated: 2022-05-12T12:50:27Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 4205–4269 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: 'Annales Henri Poincaré ' publication_identifier: eissn: - 1424-0661 issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Scattering in quantum dots via noncommutative rational functions 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 22 year: '2021' ... --- _id: '10221' abstract: - lang: eng text: We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020). acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). 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: 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, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048. doi:10.1007/s00220-021-04239-z apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04239-z chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” Communications in Mathematical Physics, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021. ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048. mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z. short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048. date_created: 2021-11-07T23:01:25Z date_published: 2021-10-29T00:00:00Z date_updated: 2023-08-14T10:29:49Z day: '29' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-021-04239-z external_id: arxiv: - '2012.13215' isi: - '000712232700001' file: - access_level: open_access checksum: a2c7b6f5d23b5453cd70d1261272283b content_type: application/pdf creator: cchlebak date_created: 2022-02-02T10:19:55Z date_updated: 2022-02-02T10:19:55Z file_id: '10715' file_name: 2021_CommunMathPhys_Cipolloni.pdf file_size: 841426 relation: main_file success: 1 file_date_updated: 2022-02-02T10:19:55Z has_accepted_license: '1' intvolume: ' 388' isi: 1 issue: '2' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1005–1048 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Eigenstate thermalization hypothesis 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 388 year: '2021' ... --- _id: '9022' abstract: - lang: eng text: "In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices." acknowledgement: I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 citation: ama: Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022 apa: Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022 chicago: Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022. ieee: G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021. ista: Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. mla: Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022. short: G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021. date_created: 2021-01-21T18:16:54Z date_published: 2021-01-25T00:00:00Z date_updated: 2023-09-07T13:29:32Z day: '25' ddc: - '510' degree_awarded: PhD department: - _id: GradSch - _id: LaEr doi: 10.15479/AT:ISTA:9022 ec_funded: 1 file: - access_level: open_access checksum: 5a93658a5f19478372523ee232887e2b content_type: application/pdf creator: gcipollo date_created: 2021-01-25T14:19:03Z date_updated: 2021-01-25T14:19:03Z file_id: '9043' file_name: thesis.pdf file_size: 4127796 relation: main_file success: 1 - access_level: closed checksum: e8270eddfe6a988e92a53c88d1d19b8c content_type: application/zip creator: gcipollo date_created: 2021-01-25T14:19:10Z date_updated: 2021-01-25T14:19:10Z file_id: '9044' file_name: Thesis_files.zip file_size: 12775206 relation: source_file file_date_updated: 2021-01-25T14:19:10Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: '380' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria 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: Fluctuations in the spectrum of random matrices type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2021' ... --- _id: '15013' abstract: - lang: eng text: We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge. acknowledgement: Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn. article_processing_charge: No article_type: original author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 citation: ama: Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221 apa: Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221 chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221. ieee: J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” Probability and Mathematical Physics, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021. ista: Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280. mla: Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221. short: J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280. date_created: 2024-02-18T23:01:03Z date_published: 2021-05-21T00:00:00Z date_updated: 2024-02-19T08:30:00Z day: '21' department: - _id: LaEr doi: 10.2140/pmp.2021.2.221 ec_funded: 1 external_id: arxiv: - '1907.13631' intvolume: ' 2' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1907.13631 month: '05' oa: 1 oa_version: Preprint page: 221-280 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Probability and Mathematical Physics publication_identifier: eissn: - 2690-1005 issn: - 2690-0998 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Spectral radius of random matrices with independent entries type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2021' ... --- _id: '8601' abstract: - lang: eng text: We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble. 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: 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, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021. ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. mla: Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7. short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021). date_created: 2020-10-04T22:01:37Z date_published: 2021-02-01T00:00:00Z date_updated: 2024-03-07T15:07:53Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00440-020-01003-7 ec_funded: 1 external_id: arxiv: - '1908.00969' isi: - '000572724600002' file: - access_level: open_access checksum: 611ae28d6055e1e298d53a57beb05ef4 content_type: application/pdf creator: dernst date_created: 2020-10-05T14:53:40Z date_updated: 2020-10-05T14:53:40Z file_id: '8612' file_name: 2020_ProbTheory_Cipolloni.pdf file_size: 497032 relation: main_file success: 1 file_date_updated: 2020-10-05T14:53:40Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: Probability Theory and Related Fields publication_identifier: eissn: - '14322064' issn: - '01788051' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Edge universality 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '7389' abstract: - lang: eng text: "Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R) is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R))." article_processing_charge: No article_type: original author: - first_name: Gyorgy Pal full_name: Geher, Gyorgy Pal last_name: Geher - first_name: Tamas full_name: Titkos, Tamas last_name: Titkos - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 2020;373(8):5855-5883. doi:10.1090/tran/8113 apa: Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/8113 chicago: Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113. ieee: G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” Transactions of the American Mathematical Society, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020. ista: Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883. mla: Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113. short: G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883. date_created: 2020-01-29T10:20:46Z date_published: 2020-08-01T00:00:00Z date_updated: 2023-08-17T14:31:03Z day: '01' ddc: - '515' department: - _id: LaEr doi: 10.1090/tran/8113 ec_funded: 1 external_id: arxiv: - '2002.00859' isi: - '000551418100018' intvolume: ' 373' isi: 1 issue: '8' keyword: - Wasserstein space - isometric embeddings - isometric rigidity - exotic isometry flow language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2002.00859 month: '08' oa: 1 oa_version: Preprint page: 5855-5883 project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability publication: Transactions of the American Mathematical Society publication_identifier: eissn: - '10886850' issn: - '00029947' publication_status: published publisher: American Mathematical Society quality_controlled: '1' status: public title: Isometric study of Wasserstein spaces - the real line type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 373 year: '2020' ... --- _id: '7512' abstract: - lang: eng text: We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have the same variance. We show that under certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory. We prove that these conditions hold for general homogeneous polynomials of degree two and for symmetrized products of independent matrices with i.i.d. entries, thus establishing the optimal bulk local law for these classes of ensembles. In particular, we generalize a similar result of Anderson for anticommutator. For more general polynomials our conditions are effectively checkable numerically. acknowledgement: "The authors are grateful to Oskari Ajanki for his invaluable help at the initial stage of this project, to Serban Belinschi for useful discussions, to Alexander Tikhomirov for calling our attention to the model example in Section 6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös: Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n" article_number: '108507' article_processing_charge: No 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: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: Yuriy full_name: Nemish, Yuriy id: 4D902E6A-F248-11E8-B48F-1D18A9856A87 last_name: Nemish orcid: 0000-0002-7327-856X citation: ama: Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 2020;278(12). doi:10.1016/j.jfa.2020.108507 apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507 chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507. ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier, 2020. ista: Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507. mla: Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” Journal of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507. short: L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020). date_created: 2020-02-23T23:00:36Z date_published: 2020-07-01T00:00:00Z date_updated: 2023-08-18T06:36:10Z day: '01' department: - _id: LaEr doi: 10.1016/j.jfa.2020.108507 ec_funded: 1 external_id: arxiv: - '1804.11340' isi: - '000522798900001' intvolume: ' 278' isi: 1 issue: '12' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.11340 month: '07' oa: 1 oa_version: Preprint project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Journal of Functional Analysis publication_identifier: eissn: - '10960783' issn: - '00221236' publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Local laws for polynomials of Wigner matrices type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 278 year: '2020' ...