--- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '19548' abstract: - lang: eng text: "We consider the BCS energy gap „.T / (essentially given by „.T / \x19 \x81.T; p\x16/,\r\nthe BCS order parameter) at all temperatures 0 \x14 T \x14 Tc up to the critical one, Tc, and show\r\nthat, in the limit of weak coupling, the ratio „.T /=Tc is given by a universal function of the relative temperature T =Tc. On the one hand, this recovers a recent result by Langmann and Triola\r\n[Phys. Rev. B 108 (2023), no. 10, article no. 104503] on three-dimensional s-wave superconductors for temperatures bounded uniformly away from Tc. On the other hand, our result lifts these\r\nrestrictions, as we consider arbitrary spatial dimensions d 2 ¹1; 2; 3º, discuss superconductors\r\nwith non-zero angular momentum (primarily in two dimensions), and treat the perhaps physically most interesting (due to the occurrence of the superconducting phase transition) regime of\r\ntemperatures close to Tc.\r\n\r\n​\r\n ." acknowledgement: "We thank Andreas Deuchert, Christian Hainzl, Edwin Langmann, Marius Lemm, Robert Seiringer, and Jan Philip Solovej for helpful discussions,\r\nand Edwin Langmann and Robert Seiringer for valuable comments on an earlier version of the manuscript.\r\nFunding. Joscha Henheik gratefully acknowledges partial financial support by the\r\nERC Advanced Grant “RMTBeyond” No. 101020331. Asbjørn Bækgaard Lauritsen\r\ngratefully acknowledges partial financial support by the Austrian Science Fund (FWF)\r\nthrough grant DOI 10.55776/I6427 (as part of the SFB/TRR 352).\r\n" article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: 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. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 2025;15(1):305–352. doi:10.4171/JST/540 apa: Henheik, S. J., & Lauritsen, A. B. (2025). Universal behavior of the BCS energy gap. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/540 chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” Journal of Spectral Theory. EMS Press, 2025. https://doi.org/10.4171/JST/540. ieee: S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,” Journal of Spectral Theory, vol. 15, no. 1. EMS Press, pp. 305–352, 2025. ista: Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352. mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” Journal of Spectral Theory, vol. 15, no. 1, EMS Press, 2025, pp. 305–352, doi:10.4171/JST/540. short: S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352. corr_author: '1' date_created: 2025-04-11T09:19:28Z date_published: 2025-01-09T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '09' ddc: - '500' department: - _id: LaEr - _id: RoSe doi: 10.4171/JST/540 ec_funded: 1 external_id: arxiv: - '2312.11310' isi: - '001438931600009' file: - access_level: open_access checksum: f49e06e8dba819f7ad52a202e287ebca content_type: application/pdf creator: cchlebak date_created: 2025-04-11T09:13:31Z date_updated: 2025-04-11T09:13:31Z file_id: '19549' file_name: Henheik_JSpectralTheory_2025.pdf file_size: 779158 relation: main_file success: 1 file_date_updated: 2025-04-11T09:13:31Z has_accepted_license: '1' intvolume: ' 15' isi: 1 issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '01' oa: 1 oa_version: Published Version page: 305–352 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: Journal of Spectral Theory publication_identifier: eissn: - 1664-0403 publication_status: published publisher: EMS Press quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Universal behavior of the BCS energy gap 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: 15 year: '2025' ... --- _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 arxiv: 1 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. 2024;37:933-973. doi:10.1007/s10959-023-01275-4 apa: Campbell, A. J., & O’Rourke, S. (2024). 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, 2024. 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, vol. 37. Springer Nature, pp. 933–973, 2024. ista: Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 37, 933–973. mla: Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability, vol. 37, Springer Nature, 2024, pp. 933–73, doi:10.1007/s10959-023-01275-4. short: A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973. corr_author: '1' date_created: 2023-08-06T22:01:13Z date_published: 2024-03-01T00:00:00Z date_updated: 2024-07-22T09:41:42Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s10959-023-01275-4 external_id: arxiv: - '2210.07927' isi: - '001038341000001' file: - access_level: open_access checksum: f7793d313104c70422140c5e6494c779 content_type: application/pdf creator: dernst date_created: 2024-07-22T09:41:21Z date_updated: 2024-07-22T09:41:21Z file_id: '17300' file_name: 2024_JourTheorProbab_Campbell.pdf file_size: 555070 relation: main_file success: 1 file_date_updated: 2024-07-22T09:41:21Z has_accepted_license: '1' intvolume: ' 37' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 933-973 publication: Journal of Theoretical Probability publication_identifier: eissn: - 1572-9230 issn: - 0894-9840 publication_status: published 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 volume: 37 year: '2024' ... --- _id: '14408' abstract: - lang: eng text: "We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0Probability Theory and Related Fields. 2024;188:1131-1182. doi:10.1007/s00440-023-01229-1 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01229-1. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” Probability Theory and Related Fields, vol. 188. Springer Nature, pp. 1131–1182, 2024. ista: Cipolloni G, Erdös L, Schröder DJ. 2024. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 188, 1131–1182. mla: Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:10.1007/s00440-023-01229-1. short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182. date_created: 2023-10-08T22:01:17Z date_published: 2024-04-01T00:00:00Z date_updated: 2025-08-05T13:28:15Z day: '01' department: - _id: LaEr doi: 10.1007/s00440-023-01229-1 ec_funded: 1 external_id: arxiv: - '2210.12060' isi: - '001118972500001' intvolume: ' 188' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2210.12060 month: '04' oa: 1 oa_version: Preprint page: 1131-1182 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Mesoscopic central limit theorem for non-Hermitian random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 188 year: '2024' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '18762' abstract: - lang: eng text: Consider the random variable $\mathrm{Tr}( f_1(W)A_1\dots f_k(W)A_k)$ where $W$ is an $N\times N$ Hermitian Wigner matrix, $k\in\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\dots, f_k$ as well as bounded deterministic matrices $A_1,\dots,A_k$. We give a functional central limit theorem showing that the fluctuations around the expectation are Gaussian. Moreover, we determine the limiting covariance structure and give explicit error bounds in terms of the scaling of $f_1,\dots,f_k$ and the number of traceless matrices among $A_1,\dots,A_k$, thus extending the results of [Cipolloni, Erdős, Schröder 2023] to products of arbitrary length $k\geq2$. As an application, we consider the fluctuation of $\mathrm{Tr}(\mathrm{e}^{\mathrm{i} tW}A_1\mathrm{e}^{-\mathrm{i} tW}A_2)$ around its thermal value $\mathrm{Tr}(A_1)\mathrm{Tr}(A_2)$ when $t$ is large and give an explicit formula for the variance. acknowledgement: "I am very grateful to László Erdős for suggesting the topic and many valuable discussions during my work on the project. I would also like to thank the two anonymous referees for their careful reading of the manuscript and detailed feedback.\r\nPartially supported by ERC Advanced Grants “RMTBeyond” No. 101020331 and “LDRaM” No. 884584." article_number: '191' article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker citation: ama: Reker J. Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. 2024;29. doi:10.1214/24-EJP1247 apa: Reker, J. (2024). Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-EJP1247 chicago: Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/24-EJP1247. ieee: J. Reker, “Multi-point functional central limit theorem for Wigner matrices,” Electronic Journal of Probability, vol. 29. Institute of Mathematical Statistics, 2024. ista: Reker J. 2024. Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. 29, 191. mla: Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” Electronic Journal of Probability, vol. 29, 191, Institute of Mathematical Statistics, 2024, doi:10.1214/24-EJP1247. short: J. Reker, Electronic Journal of Probability 29 (2024). corr_author: '1' date_created: 2025-01-05T23:01:58Z date_published: 2024-12-20T00:00:00Z date_updated: 2025-09-09T11:59:15Z day: '20' ddc: - '510' department: - _id: LaEr doi: 10.1214/24-EJP1247 ec_funded: 1 external_id: arxiv: - '2307.11028' isi: - '001381599200001' file: - access_level: open_access checksum: 67178feaa8630a332599d3037a3fe70e content_type: application/pdf creator: dernst date_created: 2025-01-08T08:44:03Z date_updated: 2025-01-08T08:44:03Z file_id: '18773' file_name: 2024_ElectrJournProbability_Reker.pdf file_size: 812428 relation: main_file success: 1 file_date_updated: 2025-01-08T08:44:03Z has_accepted_license: '1' intvolume: ' 29' isi: 1 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: Electronic Journal of Probability publication_identifier: eissn: - 1083-6489 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' related_material: record: - id: '17173' relation: earlier_version status: public scopus_import: '1' status: public title: Multi-point functional central limit theorem 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 29 year: '2024' ... --- _id: '15025' abstract: - lang: eng text: We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble. acknowledgement: The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Benjamin full_name: McKenna, Benjamin id: b0cc634c-d549-11ee-96c8-87338c7ad808 last_name: McKenna orcid: 0000-0003-2625-495X citation: ama: Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 2024;34(1B):1623-1662. doi:10.1214/23-AAP2000 apa: Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2000 chicago: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000. ieee: L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024. ista: Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662. mla: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000. short: L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662. corr_author: '1' date_created: 2024-02-25T23:00:56Z date_published: 2024-02-01T00:00:00Z date_updated: 2025-09-04T12:08:11Z day: '01' department: - _id: LaEr doi: 10.1214/23-AAP2000 ec_funded: 1 external_id: arxiv: - '2208.12206' isi: - '001163006100021' intvolume: ' 34' isi: 1 issue: 1B language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2208.12206 month: '02' oa: 1 oa_version: Preprint page: 1623-1662 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Annals of Applied Probability publication_identifier: issn: - 1050-5164 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Extremal statistics of quadratic forms of GOE/GUE eigenvectors type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 34 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15378' abstract: - lang: eng text: We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest. acknowledgement: László Erdős is partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Hong Chang Ji is supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Hong Chang full_name: Ji, Hong Chang id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d last_name: Ji citation: ama: Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 2024;77(9):3785-3840. doi:10.1002/cpa.22201 apa: Erdös, L., & Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22201 chicago: Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics. Wiley, 2024. https://doi.org/10.1002/cpa.22201. ieee: L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024. ista: Erdös L, Ji HC. 2024. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 77(9), 3785–3840. mla: Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:10.1002/cpa.22201. short: L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840. corr_author: '1' date_created: 2024-05-12T22:01:02Z date_published: 2024-09-01T00:00:00Z date_updated: 2025-09-08T07:25:47Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1002/cpa.22201 ec_funded: 1 external_id: arxiv: - '2301.04981' isi: - '001217139900001' file: - access_level: open_access checksum: fbcc9cc7bf274f024e4f4afc9c208f96 content_type: application/pdf creator: dernst date_created: 2025-01-09T09:36:41Z date_updated: 2025-01-09T09:36:41Z file_id: '18803' file_name: 2024_CommPureApplMath_Erdoes.pdf file_size: 566963 relation: main_file success: 1 file_date_updated: 2025-01-09T09:36:41Z has_accepted_license: '1' intvolume: ' 77' isi: 1 issue: '9' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '09' oa: 1 oa_version: Published Version page: 3785-3840 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Communications on Pure and Applied Mathematics publication_identifier: eissn: - 1097-0312 issn: - 0010-3640 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 77 year: '2024' ... --- _id: '17281' abstract: - lang: eng text: We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions. acknowledgement: This work was supported by the National Science Foundation [Grant No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The third author acknowledges the support of the University of Colorado Boulder, where a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin, Brian Hall, and Noah Williams for comments, corrections, and references. The authors also wish to thank the anonymous referees for useful feedback and corrections. 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 - first_name: David T full_name: Renfrew, David T id: 4845BF6A-F248-11E8-B48F-1D18A9856A87 last_name: Renfrew orcid: 0000-0003-3493-121X citation: ama: Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024;2024(13):10189-10218. doi:10.1093/imrn/rnae062 apa: Campbell, A. J., O’Rourke, S., & Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae062 chicago: Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae062. ieee: A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation,” International Mathematics Research Notices, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024. ista: Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024(13), 10189–10218. mla: Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” International Mathematics Research Notices, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:10.1093/imrn/rnae062. short: A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218. corr_author: '1' date_created: 2024-07-21T22:01:01Z date_published: 2024-07-01T00:00:00Z date_updated: 2025-09-08T08:16:32Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1093/imrn/rnae062 external_id: isi: - '001198019500001' file: - access_level: open_access checksum: f36a7dbf53f23d5833db711052e69b49 content_type: application/pdf creator: dernst date_created: 2024-07-22T06:40:19Z date_updated: 2024-07-22T06:40:19Z file_id: '17288' file_name: 2024_IMRN_Campbell.pdf file_size: 1233508 relation: main_file success: 1 file_date_updated: 2024-07-22T06:40:19Z has_accepted_license: '1' intvolume: ' 2024' isi: 1 issue: '13' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 10189-10218 publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2024 year: '2024' ... --- _id: '17375' abstract: - lang: eng text: We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion. acknowledgement: L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331. article_number: '063302' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Yuanyuan full_name: Xu, Yuanyuan id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3 last_name: Xu orcid: 0000-0003-1559-1205 citation: ama: Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 2024;65(6). doi:10.1063/5.0209705 apa: Cipolloni, G., Erdös, L., & Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0209705 chicago: Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” Journal of Mathematical Physics. AIP Publishing, 2024. https://doi.org/10.1063/5.0209705. ieee: G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” Journal of Mathematical Physics, vol. 65, no. 6. AIP Publishing, 2024. ista: Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302. mla: Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” Journal of Mathematical Physics, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:10.1063/5.0209705. short: G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024). corr_author: '1' date_created: 2024-08-04T22:01:22Z date_published: 2024-06-01T00:00:00Z date_updated: 2025-09-08T08:44:57Z day: '01' department: - _id: LaEr doi: 10.1063/5.0209705 ec_funded: 1 external_id: arxiv: - '2210.15643' isi: - '001252240700002' intvolume: ' 65' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2210.15643 month: '06' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Mathematical Physics publication_identifier: issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Precise asymptotics for the spectral radius of a large random matrix type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 65 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '18554' abstract: - lang: eng text: We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). article_number: '282' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 2024;405(12). doi:10.1007/s00220-024-05143-y apa: Erdös, L., & Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-024-05143-y chicago: Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” Communications in Mathematical Physics. Springer Nature, 2024. https://doi.org/10.1007/s00220-024-05143-y. ieee: L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” Communications in Mathematical Physics, vol. 405, no. 12. Springer Nature, 2024. ista: Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282. mla: Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” Communications in Mathematical Physics, vol. 405, no. 12, 282, Springer Nature, 2024, doi:10.1007/s00220-024-05143-y. short: L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024). corr_author: '1' date_created: 2024-11-17T23:01:46Z date_published: 2024-12-01T00:00:00Z date_updated: 2026-04-07T12:32:19Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-024-05143-y external_id: arxiv: - '2403.10359' isi: - '001348943900004' pmid: - '39526190' file: - access_level: open_access checksum: c9ae0ea195bd39b8b3a630d492fb00dc content_type: application/pdf creator: dernst date_created: 2024-11-18T08:15:07Z date_updated: 2024-11-18T08:15:07Z file_id: '18562' file_name: 2024_CommMathPhysics_Erdoes.pdf file_size: 1426046 relation: main_file success: 1 file_date_updated: 2024-11-18T08:15:07Z has_accepted_license: '1' intvolume: ' 405' isi: 1 issue: '12' language: - iso: eng month: '12' oa: 1 oa_version: Published Version pmid: 1 publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '20575' relation: dissertation_contains status: public scopus_import: '1' status: public title: Eigenstate Thermalization Hypothesis for Wigner-type matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 405 year: '2024' ... --- OA_place: repository OA_type: green _id: '18656' abstract: - lang: eng text: "We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables \r\n and \r\n in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11])." acknowledgement: LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331 article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 2024;28(6):2025-2083. doi:10.4310/ATMP.241031013250 apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.241031013250 chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2024. https://doi.org/10.4310/ATMP.241031013250. ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6. International Press, pp. 2025–2083, 2024. ista: Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083. mla: Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6, International Press, 2024, pp. 2025–83, doi:10.4310/ATMP.241031013250. short: G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083. corr_author: '1' date_created: 2024-12-15T23:01:51Z date_published: 2024-10-30T00:00:00Z date_updated: 2026-04-07T12:37:10Z day: '30' department: - _id: LaEr doi: 10.4310/ATMP.241031013250 ec_funded: 1 external_id: arxiv: - '2402.17609' intvolume: ' 28' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2402.17609 month: '10' oa: 1 oa_version: Preprint page: 2025-2083 project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Advances in Theoretical and Mathematical Physics publication_identifier: eissn: - 1095-0753 issn: - 1095-0761 publication_status: published publisher: International Press quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Out-of-time-ordered correlators for Wigner matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '17049' abstract: - lang: eng text: We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between. acknowledgement: "Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089." article_number: '110495' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 2024;287(4). doi:10.1016/j.jfa.2024.110495 apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110495 chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110495. ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” Journal of Functional Analysis, vol. 287, no. 4. Elsevier, 2024. ista: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 287(4), 110495. mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” Journal of Functional Analysis, vol. 287, no. 4, 110495, Elsevier, 2024, doi:10.1016/j.jfa.2024.110495. short: G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024). corr_author: '1' date_created: 2024-05-26T22:00:57Z date_published: 2024-08-15T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '15' ddc: - '510' department: - _id: LaEr doi: 10.1016/j.jfa.2024.110495 ec_funded: 1 external_id: isi: - '001325502400001' file: - access_level: open_access checksum: 07d3f73e0c56e68eb110851842c22ee0 content_type: application/pdf creator: dernst date_created: 2025-06-24T13:14:21Z date_updated: 2025-06-24T13:14:21Z file_id: '19891' file_name: 2025_JourFunctionalAnalysis_Cipolloni.pdf file_size: 1374854 relation: main_file success: 1 file_date_updated: 2025-06-24T13:14:21Z has_accepted_license: '1' intvolume: ' 287' isi: 1 issue: '4' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public scopus_import: '1' status: public title: Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 287 year: '2024' ... --- OA_place: repository _id: '19545' abstract: - lang: eng text: "We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling." acknowledgement: Supported by ERC Advanced Grant “RMTBeyond” No. 101020331. article_processing_charge: No arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X citation: ama: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv. doi:10.48550/arXiv.2309.05488 apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. arXiv. https://doi.org/10.48550/arXiv.2309.05488 chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.05488. ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” arXiv. . ista: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, 10.48550/arXiv.2309.05488. mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” ArXiv, doi:10.48550/arXiv.2309.05488. short: G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:19:22Z date_published: 2024-12-17T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '17' department: - _id: LaEr doi: 10.48550/arXiv.2309.05488 ec_funded: 1 external_id: arxiv: - '2309.05488' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2309.05488 month: '12' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Eigenstate thermalisation at the edge for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '19551' abstract: - lang: eng text: "We introduce a notion of a \\emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings.\r\nOn a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system.\r\nMore precisely, we say that an equilibrium state ρ0 of a Hamiltonian H0 is locally gapped in Λgap⊂Λ, whenever the Liouvillian −i[H0,⋅] is almost invertible on local observables supported in Λgap when tested in ρ0.\r\nTo put this into context, we provide other alternative notions of a local gap and discuss their relations.\r\nThe validity of response theory is based on the construction of \\emph{non-equilibrium almost stationary states} (NEASSs).\r\nBy controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \\(\\epsilon V\\) acts in a region which is further than |logϵ| away from the non-gapped region Λ∖Λgap." article_processing_charge: No arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Tom full_name: Wessel, Tom last_name: Wessel citation: ama: Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv. doi:10.48550/arXiv.2410.10809 apa: Henheik, S. J., & Wessel, T. (n.d.). Response theory for locally gapped systems. arXiv. https://doi.org/10.48550/arXiv.2410.10809 chicago: Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10809. ieee: S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” arXiv. . ista: Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv, 10.48550/arXiv.2410.10809. mla: Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” ArXiv, doi:10.48550/arXiv.2410.10809. short: S.J. Henheik, T. Wessel, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T11:54:56Z date_published: 2024-10-14T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '14' department: - _id: LaEr doi: 10.48550/arXiv.2410.10809 external_id: arxiv: - '2410.10809' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.10809 month: '10' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Response theory for locally gapped 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: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '19550' abstract: - lang: eng text: "We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band superconductor the effect of inter-band coupling can only increase\r\nthe critical temperature, irrespective of its attractive or repulsive nature\r\nand its strength. Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the dependence of the increase in critical temperature on the\r\ninter-band coupling is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands, or (2) quadratic, if there is only one dominating band." article_processing_charge: No arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Edwin full_name: Langmann, Edwin last_name: Langmann - 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, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv. doi:10.48550/arXiv.2409.17297 apa: Henheik, S. J., Langmann, E., & Lauritsen, A. B. (n.d.). Multi-band superconductors have enhanced critical temperatures. arXiv. https://doi.org/10.48550/arXiv.2409.17297 chicago: Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.17297. ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” arXiv. . ista: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv, 10.48550/arXiv.2409.17297. mla: Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” ArXiv, doi:10.48550/arXiv.2409.17297. short: S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T11:43:58Z date_published: 2024-10-21T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '21' department: - _id: LaEr - _id: RoSe doi: 10.48550/arXiv.2409.17297 external_id: arxiv: - '2409.17297' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2409.17297 month: '10' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '19540' relation: dissertation_contains status: public status: public title: Multi-band superconductors have enhanced critical temperatures tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: repository _id: '19547' abstract: - lang: eng text: "For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes." acknowledgement: "Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331." article_processing_charge: No arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv. doi:10.48550/arXiv.2410.06813 apa: Erdös, L., Henheik, S. J., & Riabov, V. (n.d.). Cusp universality for correlated random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.06813 chicago: Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.06813. ieee: L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” arXiv. . ista: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, 10.48550/arXiv.2410.06813. mla: Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.06813. short: L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:48:21Z date_published: 2024-11-03T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '03' department: - _id: LaEr doi: 10.48550/arXiv.2410.06813 ec_funded: 1 external_id: arxiv: - '2410.06813' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.06813 month: '11' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '20322' relation: later_version status: public - id: '20575' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public status: public title: Cusp universality for correlated random matrices type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: publisher OA_type: hybrid _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 arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: 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. 2024;36(9). doi:10.1142/s0129055x2360005x apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2024). 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, 2024. 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, vol. 36, no. 9. World Scientific Publishing, 2024. ista: Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005. mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:10.1142/s0129055x2360005x. short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024). corr_author: '1' date_created: 2023-11-15T23:48:14Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-04-07T13:01:40Z day: '01' ddc: - '510' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1142/s0129055x2360005x ec_funded: 1 external_id: arxiv: - '2301.05621' isi: - '001099640300002' file: - access_level: open_access checksum: 2b053a4223b4db14b90520999ec56054 content_type: application/pdf creator: dernst date_created: 2025-01-09T07:56:28Z date_updated: 2025-01-09T07:56:28Z file_id: '18786' file_name: 2024_ReviewsmathPhysics_Henheik.pdf file_size: 503910 relation: main_file success: 1 file_date_updated: 2025-01-09T07:56:28Z has_accepted_license: '1' intvolume: ' 36' isi: 1 issue: '9' 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 - _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: published publisher: World Scientific Publishing quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public - id: '18135' relation: dissertation_contains status: public 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 volume: 36 year: '2024' ... --- OA_place: publisher _id: '17164' abstract: - lang: eng text: "This thesis is structured into two parts. In the first part, we consider the random\r\nvariable X := Tr(f1(W)A1 . . . fk(W)Ak) where W is an N × N Hermitian Wigner matrix, k ∈ N, and we choose (possibly N-dependent) regular functions f1, . . . , fk as well as\r\nbounded deterministic matrices A1, . . . , Ak. In this context, we prove a functional central\r\nlimit theorem on macroscopic and mesoscopic scales, showing that the fluctuations of X\r\naround its expectation are Gaussian and that the limiting covariance structure is given\r\nby a deterministic recursion. We further give explicit error bounds in terms of the scaling\r\nof f1, . . . , fk and the number of traceless matrices among A1, . . . , Ak, thus extending\r\nthe results of Cipolloni, Erdős and Schröder [40] to products of arbitrary length k ≥ 2.\r\nAnalyzing the underlying combinatorics leads to a non-recursive formula for the variance\r\nof X as well as the covariance of X and Y := Tr(fk+1(W)Ak+1 . . . fk+ℓ(W)Ak+ℓ) of similar\r\nbuild. When restricted to polynomials, these formulas reproduce recent results of Male,\r\nMingo, Peché, and Speicher [107], showing that the underlying combinatorics of noncrossing partitions and annular non-crossing permutations continue to stay valid beyond\r\nthe setting of second-order free probability theory. As an application, we consider the\r\nfluctuation of Tr(eitW A1e\r\n−itW A2)/N around its thermal value Tr(A1) Tr(A2)/N2 when t\r\nis large and give an explicit formula for the variance.\r\nThe second part of the thesis collects three smaller projects focusing on different random\r\nmatrix models. In the first project, we show that a class of weakly perturbed Hamiltonians\r\nof the form Hλ = H0 + λW, where W is a Wigner matrix, exhibits prethermalization.\r\nThat is, the time evolution generated by Hλ relaxes to its ultimate thermal state via an\r\nintermediate prethermal state with a lifetime of order λ\r\n−2\r\n. As the main result, we obtain\r\na general relaxation formula, expressing the perturbed dynamics via the unperturbed\r\ndynamics and the ultimate thermal state. The proof relies on a two-resolvent global law\r\nfor the deformed Wigner matrix Hλ.\r\nThe second project focuses on correlated random matrices, more precisely on a correlated N × N Hermitian random matrix with a polynomially decaying metric correlation\r\nstructure. A trivial a priori bound shows that the operator norm of this model is stochastically dominated by √\r\nN. However, by calculating the trace of the moments of the matrix\r\nand using the summable decay of the cumulants, the norm estimate can be improved to a\r\nbound of order one.\r\nIn the third project, we consider a multiplicative perturbation of the form UA(t) where U\r\nis a unitary random matrix and A = diag(t, 1, ..., 1). This so-called UA model was\r\nfirst introduced by Fyodorov [73] for its applications in scattering theory. We give a\r\ngeneral description of the eigenvalue trajectories obtained by varying the parameter t and\r\nintroduce a flow of deterministic domains that separates the outlier resulting from the\r\nrank-one perturbation from the typical eigenvalues for all sub-critical timescales. The\r\nresults are obtained under generic assumptions on U that hold for various unitary random\r\nmatrices, including the circular unitary ensemble (CUE) in the original formulation of\r\nthe model." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker citation: ama: 'Reker J. Central limit theorems for random matrices: From resolvents to free probability. 2024. doi:10.15479/at:ista:17164' apa: 'Reker, J. (2024). Central limit theorems for random matrices: From resolvents to free probability. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17164' chicago: 'Reker, Jana. “Central Limit Theorems for Random Matrices: From Resolvents to Free Probability.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17164.' ieee: 'J. Reker, “Central limit theorems for random matrices: From resolvents to free probability,” Institute of Science and Technology Austria, 2024.' ista: 'Reker J. 2024. Central limit theorems for random matrices: From resolvents to free probability. Institute of Science and Technology Austria.' mla: 'Reker, Jana. Central Limit Theorems for Random Matrices: From Resolvents to Free Probability. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17164.' short: 'J. Reker, Central Limit Theorems for Random Matrices: From Resolvents to Free Probability, Institute of Science and Technology Austria, 2024.' corr_author: '1' date_created: 2024-06-24T11:23:29Z date_published: 2024-06-26T00:00:00Z date_updated: 2026-04-07T13:02:13Z day: '26' ddc: - '519' degree_awarded: PhD department: - _id: GradSch - _id: LaEr doi: 10.15479/at:ista:17164 ec_funded: 1 file: - access_level: open_access checksum: fb16d86e1f2753dc3a9e14d2bdfd84cd content_type: application/pdf creator: jreker date_created: 2024-06-26T12:39:36Z date_updated: 2024-06-26T12:44:53Z file_id: '17176' file_name: ISTA_Thesis_JReker.pdf file_size: 2783027 relation: main_file - access_level: closed checksum: cb1e54009d47c1dcf5b866c4566fa27f content_type: application/zip creator: jreker date_created: 2024-06-26T12:39:42Z date_updated: 2024-06-26T12:44:53Z file_id: '17177' file_name: ISTA_Thesis_JReker_SourceFiles.zip file_size: 3054878 relation: source_file file_date_updated: 2024-06-26T12:44:53Z has_accepted_license: '1' keyword: - Random Matrices - Spectrum - Central Limit Theorem - Resolvent - Free Probability language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '06' oa: 1 oa_version: Published Version page: '206' project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '17173' relation: part_of_dissertation status: public - id: '11135' relation: part_of_dissertation status: public - id: '17047' relation: part_of_dissertation status: public - id: '17154' relation: part_of_dissertation status: public - id: '17174' relation: part_of_dissertation status: public status: public supervisor: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 title: 'Central limit theorems for random matrices: From resolvents to free probability' tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- _id: '17154' abstract: - lang: eng text: We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of Male et al. (Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419, 2023). and thus allow identifying the fluctuation around the thermal value in certain thermalization problems. article_number: '10' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker citation: ama: Reker J. Fluctuation moments for regular functions of Wigner Matrices. Mathematical Physics, Analysis and Geometry. 2024;27(3). doi:10.1007/s11040-024-09483-y apa: Reker, J. (2024). Fluctuation moments for regular functions of Wigner Matrices. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-024-09483-y chicago: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2024. https://doi.org/10.1007/s11040-024-09483-y. ieee: J. Reker, “Fluctuation moments for regular functions of Wigner Matrices,” Mathematical Physics, Analysis and Geometry, vol. 27, no. 3. Springer Nature, 2024. ista: Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices. Mathematical Physics, Analysis and Geometry. 27(3), 10. mla: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.” Mathematical Physics, Analysis and Geometry, vol. 27, no. 3, 10, Springer Nature, 2024, doi:10.1007/s11040-024-09483-y. short: J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024). date_created: 2024-06-21T09:31:17Z date_published: 2024-06-20T00:00:00Z date_updated: 2026-04-07T13:02:12Z day: '20' ddc: - '519' department: - _id: LaEr doi: 10.1007/s11040-024-09483-y ec_funded: 1 external_id: arxiv: - '2307.11029' isi: - '001251464300001' file: - access_level: open_access checksum: 7d04318d66f765621bdcb648378d458e content_type: application/pdf creator: cchlebak date_created: 2024-06-26T11:26:42Z date_updated: 2024-06-26T11:26:42Z file_id: '17175' file_name: 2024_MathPhysAnaGeo_Reker.pdf file_size: 1327596 relation: main_file success: 1 file_date_updated: 2024-06-26T11:26:42Z has_accepted_license: '1' intvolume: ' 27' isi: 1 issue: '3' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Mathematical Physics, Analysis and Geometry publication_identifier: eissn: - 1572-9656 issn: - 1385-0172 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '17164' relation: dissertation_contains status: public scopus_import: '1' status: public title: Fluctuation moments for regular functions 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 27 year: '2024' ... --- OA_place: repository OA_type: green _id: '17047' abstract: - lang: eng text: We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random matrix models. article_number: '2450007' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker citation: ama: 'Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. 2024;13(2). doi:10.1142/s2010326324500072' apa: 'Dubach, G., & Reker, J. (2024). Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326324500072' chicago: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” Random Matrices: Theory and Applications. World Scientific Publishing, 2024. https://doi.org/10.1142/s2010326324500072.' ieee: 'G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation of a unitary matrix,” Random Matrices: Theory and Applications, vol. 13, no. 2. World Scientific Publishing, 2024.' ista: 'Dubach G, Reker J. 2024. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. 13(2), 2450007.' mla: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” Random Matrices: Theory and Applications, vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:10.1142/s2010326324500072.' short: 'G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).' corr_author: '1' date_created: 2024-05-23T08:31:57Z date_published: 2024-04-01T00:00:00Z date_updated: 2026-04-07T13:02:12Z day: '01' department: - _id: GradSch - _id: LaEr doi: 10.1142/s2010326324500072 ec_funded: 1 external_id: arxiv: - '2212.14638' isi: - '001229295200002' intvolume: ' 13' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2212.14638' month: '04' 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: 'Random Matrices: Theory and Applications' publication_identifier: eissn: - 2010-3271 issn: - 2010-3263 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' related_material: record: - id: '17164' relation: dissertation_contains status: public scopus_import: '1' status: public title: Dynamics of a rank-one multiplicative perturbation of a unitary matrix type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 13 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 arxiv: 1 author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: 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. corr_author: '1' date_created: 2022-08-07T22:02:00Z date_published: 2023-04-01T00:00:00Z date_updated: 2024-10-09T21:03:02Z 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' ...