[{"publisher":"Springer Nature","doi":"10.1007/s10959-023-01275-4","file_date_updated":"2024-07-22T09:41:21Z","_id":"13975","day":"01","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","fulldoi":"https://doi.org/10.1007/s10959-023-01275-4","has_accepted_license":"1","volume":37,"date_published":"2024-03-01T00:00:00Z","publication_status":"published","author":[{"first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","last_name":"Campbell","full_name":"Campbell, Andrew J"},{"last_name":"O’Rourke","full_name":"O’Rourke, Sean","first_name":"Sean"}],"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)","title":"Spectrum of Lévy–Khintchine random laplacian matrices","intvolume":"        37","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"status":"public","page":"933-973","publication":"Journal of Theoretical Probability","month":"03","external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"oa_version":"Published Version","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"scopus_import":"1","corr_author":"1","type":"journal_article","publication_identifier":{"issn":["0894-9840"],"eissn":["1572-9230"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","citation":{"ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. 2024;37:933-973. doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973.","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>, vol. 37, Springer Nature, 2024, pp. 933–73, doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>.","apa":"Campbell, A. J., &#38; O’Rourke, S. (2024). Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>","ista":"Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 37, 933–973.","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” <i>Journal of Theoretical Probability</i>, vol. 37. Springer Nature, pp. 933–973, 2024.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>."},"oa":1,"arxiv":1,"date_created":"2023-08-06T22:01:13Z","file":[{"file_id":"17300","date_updated":"2024-07-22T09:41:21Z","file_name":"2024_JourTheorProbab_Campbell.pdf","relation":"main_file","success":1,"date_created":"2024-07-22T09:41:21Z","access_level":"open_access","file_size":555070,"content_type":"application/pdf","checksum":"f7793d313104c70422140c5e6494c779","creator":"dernst"}],"ddc":["510"],"article_type":"original","isi":1,"date_updated":"2024-07-22T09:41:42Z"},{"publication":"Probability Theory and Related Fields","page":"1131-1182","status":"public","ec_funded":1,"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","intvolume":"       188","article_processing_charge":"No","acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.\r\nLászló Erdős supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Dominik Schröder supported by the SNSF Ambizione Grant PZ00P2 209089.","publication_status":"published","author":[{"first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"date_published":"2024-04-01T00:00:00Z","volume":188,"fulldoi":"https://doi.org/10.1007/s00440-023-01229-1","quality_controlled":"1","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 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator."}],"day":"01","_id":"14408","doi":"10.1007/s00440-023-01229-1","publisher":"Springer Nature","date_updated":"2025-08-05T13:28:15Z","article_type":"original","isi":1,"date_created":"2023-10-08T22:01:17Z","arxiv":1,"oa":1,"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>, vol. 188. Springer Nature, pp. 1131–1182, 2024.","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.” <i>Probability Theory and Related Fields</i>, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182.","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2024;188:1131-1182. doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>"},"year":"2024","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.12060","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","external_id":{"isi":["001118972500001"],"arxiv":["2210.12060"]},"month":"04"},{"arxiv":1,"date_created":"2024-02-25T23:00:56Z","oa":1,"citation":{"ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” <i>Annals of Applied Probability</i>, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. 2024;34(1B):1623-1662. doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>","mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>.","apa":"Erdös, L., &#38; McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662."},"isi":1,"article_type":"original","date_updated":"2025-09-04T12:08:11Z","scopus_import":"1","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2208.12206","open_access":"1"}],"month":"02","external_id":{"arxiv":["2208.12206"],"isi":["001163006100021"]},"year":"2024","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","corr_author":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"issn":["1050-5164"]},"author":[{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"id":"b0cc634c-d549-11ee-96c8-87338c7ad808","full_name":"McKenna, Benjamin","last_name":"McKenna","orcid":"0000-0003-2625-495X","first_name":"Benjamin"}],"publication_status":"published","title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","intvolume":"        34","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","date_published":"2024-02-01T00:00:00Z","volume":34,"ec_funded":1,"department":[{"_id":"LaEr"}],"publication":"Annals of Applied Probability","status":"public","page":"1623-1662","language":[{"iso":"eng"}],"_id":"15025","doi":"10.1214/23-AAP2000","publisher":"Institute of Mathematical Statistics","fulldoi":"https://doi.org/10.1214/23-AAP2000","issue":"1B","abstract":[{"text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble.","lang":"eng"}],"day":"01","quality_controlled":"1"},{"volume":77,"date_published":"2024-09-01T00:00:00Z","publication_status":"published","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","intvolume":"        77","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","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.","language":[{"iso":"eng"}],"ec_funded":1,"department":[{"_id":"LaEr"}],"publication":"Communications on Pure and Applied Mathematics","status":"public","page":"3785-3840","OA_place":"publisher","file_date_updated":"2025-01-09T09:36:41Z","doi":"10.1002/cpa.22201","publisher":"Wiley","_id":"15378","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","abstract":[{"text":"We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest.","lang":"eng"}],"day":"01","quality_controlled":"1","fulldoi":"https://doi.org/10.1002/cpa.22201","has_accepted_license":"1","issue":"9","oa":1,"citation":{"short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840.","ama":"Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2024;77(9):3785-3840. doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>","mla":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>.","apa":"Erdös, L., &#38; Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>","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.","ieee":"L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024.","chicago":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2024. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>."},"arxiv":1,"date_created":"2024-05-12T22:01:02Z","file":[{"file_size":566963,"content_type":"application/pdf","access_level":"open_access","date_created":"2025-01-09T09:36:41Z","success":1,"creator":"dernst","checksum":"fbcc9cc7bf274f024e4f4afc9c208f96","file_name":"2024_CommPureApplMath_Erdoes.pdf","file_id":"18803","date_updated":"2025-01-09T09:36:41Z","relation":"main_file"}],"ddc":["510"],"article_type":"original","isi":1,"date_updated":"2025-09-08T07:25:47Z","month":"09","external_id":{"arxiv":["2301.04981"],"isi":["001217139900001"]},"scopus_import":"1","tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)"},"oa_version":"Published Version","corr_author":"1","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"year":"2024","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}]},{"type":"journal_article","corr_author":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"year":"2024","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"month":"04","external_id":{"arxiv":["2212.14638"],"isi":["001229295200002"]},"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2212.14638","open_access":"1"}],"article_type":"original","isi":1,"date_updated":"2026-04-07T13:02:12Z","citation":{"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.","apa":"Dubach, G., &#38; Reker, J. (2024). Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326324500072\">https://doi.org/10.1142/s2010326324500072</a>","mla":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>, vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>.","ama":"Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. 2024;13(2). doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>","short":"G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).","chicago":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s2010326324500072\">https://doi.org/10.1142/s2010326324500072</a>.","ieee":"G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation of a unitary matrix,” <i>Random Matrices: Theory and Applications</i>, vol. 13, no. 2. World Scientific Publishing, 2024."},"oa":1,"arxiv":1,"date_created":"2024-05-23T08:31:57Z","day":"01","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","issue":"2","fulldoi":"https://doi.org/10.1142/s2010326324500072","OA_place":"repository","publisher":"World Scientific Publishing","doi":"10.1142/s2010326324500072","_id":"17047","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"17164","relation":"dissertation_contains","status":"public"}]},"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ec_funded":1,"status":"public","article_number":"2450007","publication":"Random Matrices: Theory and Applications","date_published":"2024-04-01T00:00:00Z","volume":13,"author":[{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume"},{"last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","first_name":"Jana"}],"publication_status":"published","OA_type":"green","article_processing_charge":"No","intvolume":"        13","title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix"},{"_id":"17154","publisher":"Springer Nature","doi":"10.1007/s11040-024-09483-y","file_date_updated":"2024-06-26T11:26:42Z","fulldoi":"https://doi.org/10.1007/s11040-024-09483-y","has_accepted_license":"1","issue":"3","day":"20","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."}],"quality_controlled":"1","author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","full_name":"Reker, Jana","first_name":"Jana"}],"publication_status":"published","article_processing_charge":"Yes (via OA deal)","intvolume":"        27","title":"Fluctuation moments for regular functions of Wigner Matrices","volume":27,"date_published":"2024-06-20T00:00:00Z","department":[{"_id":"LaEr"}],"ec_funded":1,"status":"public","publication":"Mathematical Physics, Analysis and Geometry","article_number":"10","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"17164"}]},"oa_version":"Published Version","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"scopus_import":"1","month":"06","external_id":{"arxiv":["2307.11029"],"isi":["001251464300001"]},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2024","type":"journal_article","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"date_created":"2024-06-21T09:31:17Z","file":[{"relation":"main_file","date_updated":"2024-06-26T11:26:42Z","file_id":"17175","file_name":"2024_MathPhysAnaGeo_Reker.pdf","checksum":"7d04318d66f765621bdcb648378d458e","creator":"cchlebak","success":1,"date_created":"2024-06-26T11:26:42Z","access_level":"open_access","file_size":1327596,"content_type":"application/pdf"}],"citation":{"apa":"Reker, J. (2024). Fluctuation moments for regular functions of Wigner Matrices. <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11040-024-09483-y\">https://doi.org/10.1007/s11040-024-09483-y</a>","mla":"Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3, 10, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s11040-024-09483-y\">10.1007/s11040-024-09483-y</a>.","ista":"Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices. Mathematical Physics, Analysis and Geometry. 27(3), 10.","ama":"Reker J. Fluctuation moments for regular functions of Wigner Matrices. <i>Mathematical Physics, Analysis and Geometry</i>. 2024;27(3). doi:<a href=\"https://doi.org/10.1007/s11040-024-09483-y\">10.1007/s11040-024-09483-y</a>","short":"J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024).","chicago":"Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s11040-024-09483-y\">https://doi.org/10.1007/s11040-024-09483-y</a>.","ieee":"J. Reker, “Fluctuation moments for regular functions of Wigner Matrices,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3. Springer Nature, 2024."},"oa":1,"article_type":"original","isi":1,"date_updated":"2026-04-07T13:02:12Z","ddc":["519"]},{"doi":"10.15479/at:ista:17164","file_date_updated":"2024-06-26T12:44:53Z","publisher":"Institute of Science and Technology Austria","degree_awarded":"PhD","OA_place":"publisher","keyword":["Random Matrices","Spectrum","Central Limit Theorem","Resolvent","Free Probability"],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","_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."}],"day":"26","has_accepted_license":"1","fulldoi":"https://doi.org/10.15479/at:ista:17164","date_published":"2024-06-26T00:00:00Z","title":"Central limit theorems for random matrices: From resolvents to free probability","article_processing_charge":"No","author":[{"first_name":"Jana","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker"}],"publication_status":"published","related_material":{"record":[{"status":"public","id":"17173","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"11135","status":"public"},{"status":"public","id":"17047","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"17154","status":"public"},{"id":"17174","relation":"part_of_dissertation","status":"public"}]},"language":[{"iso":"eng"}],"status":"public","page":"206","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"month":"06","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","publication_identifier":{"issn":["2663-337X"]},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","type":"dissertation","corr_author":"1","year":"2024","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"oa":1,"citation":{"ama":"Reker J. Central limit theorems for random matrices: From resolvents to free probability. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17164\">10.15479/at:ista:17164</a>","short":"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.","apa":"Reker, J. (2024). <i>Central limit theorems for random matrices: From resolvents to free probability</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17164\">https://doi.org/10.15479/at:ista:17164</a>","mla":"Reker, Jana. <i>Central Limit Theorems for Random Matrices: From Resolvents to Free Probability</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17164\">10.15479/at:ista:17164</a>.","ieee":"J. Reker, “Central limit theorems for random matrices: From resolvents to free probability,” Institute of Science and Technology Austria, 2024.","chicago":"Reker, Jana. “Central Limit Theorems for Random Matrices: From Resolvents to Free Probability.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17164\">https://doi.org/10.15479/at:ista:17164</a>."},"date_created":"2024-06-24T11:23:29Z","file":[{"date_created":"2024-06-26T12:39:36Z","access_level":"open_access","content_type":"application/pdf","file_size":2783027,"checksum":"fb16d86e1f2753dc3a9e14d2bdfd84cd","creator":"jreker","file_id":"17176","date_updated":"2024-06-26T12:44:53Z","file_name":"ISTA_Thesis_JReker.pdf","relation":"main_file"},{"file_id":"17177","date_updated":"2024-06-26T12:44:53Z","file_name":"ISTA_Thesis_JReker_SourceFiles.zip","relation":"source_file","date_created":"2024-06-26T12:39:42Z","content_type":"application/zip","file_size":3054878,"access_level":"closed","checksum":"cb1e54009d47c1dcf5b866c4566fa27f","creator":"jreker"}],"ddc":["519"],"supervisor":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"}],"date_updated":"2026-04-07T13:02:13Z"},{"has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s00220-024-05143-y","issue":"12","day":"01","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."}],"quality_controlled":"1","_id":"18554","OA_place":"publisher","publisher":"Springer Nature","file_date_updated":"2024-11-18T08:15:07Z","doi":"10.1007/s00220-024-05143-y","department":[{"_id":"LaEr"}],"status":"public","publication":"Communications in Mathematical Physics","article_number":"282","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"20575","relation":"dissertation_contains","status":"public"}]},"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"first_name":"Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr"}],"publication_status":"published","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices","intvolume":"       405","date_published":"2024-12-01T00:00:00Z","volume":405,"pmid":1,"year":"2024","corr_author":"1","type":"journal_article","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"scopus_import":"1","month":"12","external_id":{"isi":["001348943900004"],"arxiv":["2403.10359"],"pmid":["39526190"]},"article_type":"original","isi":1,"date_updated":"2026-04-07T12:32:19Z","ddc":["510"],"arxiv":1,"file":[{"relation":"main_file","file_name":"2024_CommMathPhysics_Erdoes.pdf","date_updated":"2024-11-18T08:15:07Z","file_id":"18562","creator":"dernst","checksum":"c9ae0ea195bd39b8b3a630d492fb00dc","content_type":"application/pdf","file_size":1426046,"access_level":"open_access","date_created":"2024-11-18T08:15:07Z","success":1}],"date_created":"2024-11-17T23:01:46Z","citation":{"ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282.","apa":"Erdös, L., &#38; Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>","mla":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12, 282, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>.","short":"L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).","ama":"Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. 2024;405(12). doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>","chicago":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>.","ieee":"L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12. Springer Nature, 2024."},"oa":1},{"date_published":"2024-12-20T00:00:00Z","volume":29,"intvolume":"        29","title":"Multi-point functional central limit theorem for Wigner matrices","article_processing_charge":"Yes","OA_type":"gold","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.","publication_status":"published","author":[{"first_name":"Jana","full_name":"Reker, Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"related_material":{"record":[{"id":"17173","relation":"earlier_version","status":"public"}]},"language":[{"iso":"eng"}],"publication":"Electronic Journal of Probability","article_number":"191","status":"public","ec_funded":1,"department":[{"_id":"LaEr"}],"file_date_updated":"2025-01-08T08:44:03Z","doi":"10.1214/24-EJP1247","publisher":"Institute of Mathematical Statistics","OA_place":"publisher","_id":"18762","quality_controlled":"1","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."}],"day":"20","fulldoi":"https://doi.org/10.1214/24-EJP1247","has_accepted_license":"1","oa":1,"citation":{"ieee":"J. Reker, “Multi-point functional central limit theorem for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 29. Institute of Mathematical Statistics, 2024.","chicago":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/24-EJP1247\">https://doi.org/10.1214/24-EJP1247</a>.","short":"J. Reker, Electronic Journal of Probability 29 (2024).","ama":"Reker J. Multi-point functional central limit theorem for Wigner matrices. <i>Electronic Journal of Probability</i>. 2024;29. doi:<a href=\"https://doi.org/10.1214/24-EJP1247\">10.1214/24-EJP1247</a>","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.” <i>Electronic Journal of Probability</i>, vol. 29, 191, Institute of Mathematical Statistics, 2024, doi:<a href=\"https://doi.org/10.1214/24-EJP1247\">10.1214/24-EJP1247</a>.","apa":"Reker, J. (2024). Multi-point functional central limit theorem for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/24-EJP1247\">https://doi.org/10.1214/24-EJP1247</a>"},"date_created":"2025-01-05T23:01:58Z","file":[{"access_level":"open_access","file_size":812428,"content_type":"application/pdf","success":1,"date_created":"2025-01-08T08:44:03Z","creator":"dernst","checksum":"67178feaa8630a332599d3037a3fe70e","file_name":"2024_ElectrJournProbability_Reker.pdf","date_updated":"2025-01-08T08:44:03Z","file_id":"18773","relation":"main_file"}],"arxiv":1,"ddc":["510"],"date_updated":"2025-09-09T11:59:15Z","article_type":"original","isi":1,"external_id":{"isi":["001381599200001"],"arxiv":["2307.11028"]},"month":"12","DOAJ_listed":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"scopus_import":"1","oa_version":"Published Version","publication_identifier":{"eissn":["1083-6489"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","corr_author":"1","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"year":"2024"},{"oa":1,"citation":{"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.","apa":"Campbell, A. J., O’Rourke, S., &#38; Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>","mla":"Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>.","ama":"Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. 2024;2024(13):10189-10218. doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218.","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.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>.","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,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024."},"file":[{"creator":"dernst","checksum":"f36a7dbf53f23d5833db711052e69b49","access_level":"open_access","content_type":"application/pdf","file_size":1233508,"success":1,"date_created":"2024-07-22T06:40:19Z","relation":"main_file","file_name":"2024_IMRN_Campbell.pdf","date_updated":"2024-07-22T06:40:19Z","file_id":"17288"}],"date_created":"2024-07-21T22:01:01Z","ddc":["510"],"date_updated":"2025-09-08T08:16:32Z","isi":1,"article_type":"original","external_id":{"isi":["001198019500001"]},"month":"07","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"scopus_import":"1","oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"type":"journal_article","corr_author":"1","year":"2024","volume":2024,"date_published":"2024-07-01T00:00:00Z","intvolume":"      2024","title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","article_processing_charge":"Yes (via OA deal)","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.","author":[{"last_name":"Campbell","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","full_name":"Campbell, Andrew J","first_name":"Andrew J"},{"full_name":"O'Rourke, Sean","last_name":"O'Rourke","first_name":"Sean"},{"orcid":"0000-0003-3493-121X","full_name":"Renfrew, David T","last_name":"Renfrew","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","first_name":"David T"}],"publication_status":"published","language":[{"iso":"eng"}],"publication":"International Mathematics Research Notices","status":"public","page":"10189-10218","department":[{"_id":"LaEr"}],"doi":"10.1093/imrn/rnae062","file_date_updated":"2024-07-22T06:40:19Z","publisher":"Oxford University Press","_id":"17281","quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"day":"01","fulldoi":"https://doi.org/10.1093/imrn/rnae062","has_accepted_license":"1","issue":"13"},{"publication_status":"published","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan"}],"title":"Precise asymptotics for the spectral radius of a large random matrix","intvolume":"        65","article_processing_charge":"No","acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","date_published":"2024-06-01T00:00:00Z","volume":65,"ec_funded":1,"department":[{"_id":"LaEr"}],"article_number":"063302","publication":"Journal of Mathematical Physics","status":"public","language":[{"iso":"eng"}],"_id":"17375","doi":"10.1063/5.0209705","publisher":"AIP Publishing","issue":"6","fulldoi":"https://doi.org/10.1063/5.0209705","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."}],"day":"01","quality_controlled":"1","arxiv":1,"date_created":"2024-08-04T22:01:22Z","oa":1,"citation":{"ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6. AIP Publishing, 2024.","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2024. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","ama":"Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. 2024;65(6). doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>","ista":"Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.","apa":"Cipolloni, G., Erdös, L., &#38; Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>","mla":"Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>."},"isi":1,"article_type":"original","date_updated":"2025-09-08T08:44:57Z","scopus_import":"1","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.15643"}],"month":"06","external_id":{"arxiv":["2210.15643"],"isi":["001252240700002"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"year":"2024","corr_author":"1","type":"journal_article","publication_identifier":{"issn":["0022-2488"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"month":"12","external_id":{"arxiv":["2309.05488"]},"oa_version":"Preprint","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.05488","open_access":"1"}],"corr_author":"1","type":"preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2024","citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","ama":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>.","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. ."},"oa":1,"arxiv":1,"date_created":"2025-04-11T08:19:22Z","date_updated":"2026-07-29T13:18:16Z","OA_place":"repository","doi":"10.48550/arXiv.2309.05488","_id":"19545","day":"17","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling."}],"fulldoi":"https://doi.org/10.48550/arXiv.2309.05488","date_published":"2024-12-17T00:00:00Z","author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X"}],"publication_status":"draft","article_processing_charge":"No","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","title":"Eigenstate thermalisation at the edge for Wigner matrices","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"department":[{"_id":"LaEr"}],"ec_funded":1,"status":"public","publication":"arXiv"},{"author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"full_name":"Langmann, Edwin","last_name":"Langmann","first_name":"Edwin"},{"first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","orcid":"0000-0003-4476-2288"}],"publication_status":"draft","arxiv":1,"article_processing_charge":"No","title":"Multi-band superconductors have enhanced critical temperatures","date_created":"2025-04-11T11:43:58Z","citation":{"ista":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>.","apa":"Henheik, S. J., Langmann, E., &#38; Lauritsen, A. B. (n.d.). Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">https://doi.org/10.48550/arXiv.2409.17297</a>","mla":"Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>.","ama":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","chicago":"Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">https://doi.org/10.48550/arXiv.2409.17297</a>.","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>arXiv</i>. ."},"oa":1,"date_published":"2024-10-21T00:00:00Z","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"status":"public","date_updated":"2026-07-29T13:18:16Z","publication":"arXiv","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"22290"},{"status":"public","relation":"dissertation_contains","id":"19540"}]},"oa_version":"Preprint","_id":"19550","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.17297","open_access":"1"}],"month":"10","OA_place":"repository","external_id":{"arxiv":["2409.17297"]},"doi":"10.48550/arXiv.2409.17297","fulldoi":"https://doi.org/10.48550/arXiv.2409.17297","year":"2024","day":"21","type":"preprint","abstract":[{"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.","lang":"eng"}],"corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"oa_version":"Published Version","scopus_import":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"external_id":{"isi":["001325502400001"]},"month":"08","year":"2024","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","corr_author":"1","date_created":"2024-05-26T22:00:57Z","file":[{"checksum":"07d3f73e0c56e68eb110851842c22ee0","creator":"dernst","date_created":"2025-06-24T13:14:21Z","success":1,"file_size":1374854,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_updated":"2025-06-24T13:14:21Z","file_id":"19891","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf"}],"citation":{"mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 287, no. 4, 110495, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>","ista":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 287(4), 110495.","ama":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2024;287(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>","short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024).","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>.","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 287, no. 4. Elsevier, 2024."},"oa":1,"date_updated":"2026-07-29T13:18:17Z","isi":1,"article_type":"original","ddc":["510"],"_id":"17049","publisher":"Elsevier","file_date_updated":"2025-06-24T13:14:21Z","doi":"10.1016/j.jfa.2024.110495","OA_place":"publisher","has_accepted_license":"1","fulldoi":"https://doi.org/10.1016/j.jfa.2024.110495","issue":"4","quality_controlled":"1","day":"15","abstract":[{"text":"We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","OA_type":"hybrid","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","intvolume":"       287","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"publication_status":"published","volume":287,"date_published":"2024-08-15T00:00:00Z","status":"public","article_number":"110495","publication":"Journal of Functional Analysis","department":[{"_id":"LaEr"}],"ec_funded":1,"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]}},{"date_published":"2024-10-01T00:00:00Z","volume":36,"author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen"},{"first_name":"Barbara","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","last_name":"Roos","id":"5DA90512-D80F-11E9-8994-2E2EE6697425"}],"publication_status":"published","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.","OA_type":"hybrid","article_processing_charge":"Yes (in subscription journal)","intvolume":"        36","title":"Universality in low-dimensional BCS theory","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"18135","relation":"dissertation_contains"},{"status":"public","id":"19540","relation":"dissertation_contains"}]},"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"ec_funded":1,"status":"public","article_number":"2360005 ","publication":"Reviews in Mathematical Physics","OA_place":"publisher","publisher":"World Scientific Publishing","doi":"10.1142/s0129055x2360005x","file_date_updated":"2025-01-09T07:56:28Z","_id":"14542","day":"01","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."}],"quality_controlled":"1","issue":"9","fulldoi":"https://doi.org/10.1142/s0129055x2360005x","has_accepted_license":"1","citation":{"ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2024;36(9). doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2024). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>.","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9. World Scientific Publishing, 2024.","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>."},"oa":1,"arxiv":1,"date_created":"2023-11-15T23:48:14Z","file":[{"file_id":"18786","date_updated":"2025-01-09T07:56:28Z","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","relation":"main_file","date_created":"2025-01-09T07:56:28Z","success":1,"file_size":503910,"content_type":"application/pdf","access_level":"open_access","checksum":"2b053a4223b4db14b90520999ec56054","creator":"dernst"}],"ddc":["510"],"isi":1,"article_type":"original","date_updated":"2026-07-29T13:18:16Z","month":"10","external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"oa_version":"Published Version","scopus_import":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"corr_author":"1","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"year":"2024"},{"OA_place":"repository","doi":"10.4310/ATMP.241031013250","publisher":"International Press of Boston","_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])."}],"day":"30","quality_controlled":"1","issue":"6","fulldoi":"https://doi.org/10.4310/ATMP.241031013250","das_tickbox":"1","volume":28,"date_published":"2024-10-30T00:00:00Z","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha"}],"publication_status":"published","title":"Out-of-time-ordered correlators for Wigner matrices","intvolume":"        28","acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","article_processing_charge":"No","OA_type":"green","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"language":[{"iso":"eng"}],"ec_funded":1,"department":[{"_id":"LaEr"}],"publication":"Advances in Theoretical and Mathematical Physics","status":"public","page":"2025-2083","month":"10","external_id":{"arxiv":["2402.17609"]},"scopus_import":"1","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.17609"}],"type":"journal_article","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1095-0761"],"eissn":["1095-0753"]},"year":"2024","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"oa":1,"citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2024;28(6):2025-2083. doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083.","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.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6, International Press of Boston, 2024, pp. 2025–83, doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6. International Press of Boston, pp. 2025–2083, 2024.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press of Boston, 2024. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>."},"arxiv":1,"date_created":"2024-12-15T23:01:51Z","article_type":"original","date_updated":"2026-07-29T13:18:17Z"},{"author":[{"full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha"},{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov","full_name":"Riabov, Volodymyr"}],"publication_status":"draft","article_processing_charge":"No","acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","title":"Cusp universality for correlated random matrices","date_published":"2024-11-03T00:00:00Z","department":[{"_id":"LaEr"}],"ec_funded":1,"status":"public","publication":"arXiv","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"later_version","id":"20322","status":"public"},{"status":"public","id":"20575","relation":"dissertation_contains"},{"id":"19540","relation":"dissertation_contains","status":"public"}]},"_id":"19547","OA_place":"repository","doi":"10.48550/arXiv.2410.06813","fulldoi":"https://doi.org/10.48550/arXiv.2410.06813","day":"03","abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes.","lang":"eng"}],"arxiv":1,"date_created":"2025-04-11T08:48:21Z","citation":{"chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>.","ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>arXiv</i>. .","ista":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>.","apa":"Erdös, L., Henheik, S. J., &#38; Riabov, V. (n.d.). Cusp universality for correlated random matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>.","short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>"},"oa":1,"date_updated":"2026-07-29T13:18:17Z","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.06813","open_access":"1"}],"month":"11","external_id":{"arxiv":["2410.06813"]},"year":"2024","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"corr_author":"1","type":"preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"publication":"arXiv","date_updated":"2026-07-29T13:18:16Z","status":"public","oa":1,"date_published":"2024-10-14T00:00:00Z","citation":{"ista":"Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.10809\">10.48550/arXiv.2410.10809</a>.","apa":"Henheik, S. J., &#38; Wessel, T. (n.d.). Response theory for locally gapped systems. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.10809\">https://doi.org/10.48550/arXiv.2410.10809</a>","mla":"Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10809\">10.48550/arXiv.2410.10809</a>.","short":"S.J. Henheik, T. Wessel, ArXiv (n.d.).","ama":"Henheik SJ, Wessel T. Response theory for locally gapped systems. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10809\">10.48550/arXiv.2410.10809</a>","chicago":"Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.10809\">https://doi.org/10.48550/arXiv.2410.10809</a>.","ieee":"S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” <i>arXiv</i>. ."},"arxiv":1,"author":[{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"first_name":"Tom","full_name":"Wessel, Tom","last_name":"Wessel"}],"publication_status":"draft","date_created":"2025-04-11T11:54:56Z","title":"Response theory for locally gapped systems","article_processing_charge":"No","corr_author":"1","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."}],"type":"preprint","day":"14","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","fulldoi":"https://doi.org/10.48550/arXiv.2410.10809","year":"2024","OA_place":"repository","month":"10","doi":"10.48550/arXiv.2410.10809","external_id":{"arxiv":["2410.10809"]},"_id":"19551","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.10809"}]},{"month":"04","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"oa_version":"Published Version","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"scopus_import":"1","corr_author":"1","type":"journal_article","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","citation":{"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.” <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","ama":"Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 185. Springer Nature, pp. 1183–1218, 2023."},"oa":1,"arxiv":1,"date_created":"2022-08-07T22:02:00Z","file":[{"relation":"main_file","file_id":"14054","date_updated":"2023-08-14T12:47:32Z","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","checksum":"b9247827dae5544d1d19c37abe547abc","creator":"dernst","date_created":"2023-08-14T12:47:32Z","success":1,"content_type":"application/pdf","file_size":782278,"access_level":"open_access"}],"ddc":["510"],"isi":1,"article_type":"original","date_updated":"2024-10-09T21:03:02Z","publisher":"Springer Nature","doi":"10.1007/s00440-022-01156-7","file_date_updated":"2023-08-14T12:47:32Z","_id":"11741","day":"01","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s00440-022-01156-7","volume":185,"date_published":"2023-04-01T00:00:00Z","publication_status":"published","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"article_processing_charge":"Yes (via OA deal)","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).","title":"Quenched universality for deformed Wigner matrices","intvolume":"       185","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"page":"1183–1218","status":"public","publication":"Probability Theory and Related Fields"},{"article_type":"original","isi":1,"date_updated":"2025-04-14T07:44:00Z","ddc":["510"],"arxiv":1,"date_created":"2023-02-26T23:01:01Z","file":[{"file_name":"2023_ElectCommProbability_Dubach.pdf","date_updated":"2023-02-27T09:43:27Z","file_id":"12692","relation":"main_file","file_size":479105,"content_type":"application/pdf","access_level":"open_access","date_created":"2023-02-27T09:43:27Z","success":1,"creator":"dernst","checksum":"a1c6f0a3e33688fd71309c86a9aad86e"}],"oa":1,"citation":{"ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>."},"year":"2023","project":[{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"corr_author":"1","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1083-589X"]},"scopus_import":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"oa_version":"Published Version","month":"02","external_id":{"arxiv":["2108.13694"],"isi":["000950650200005"]},"ec_funded":1,"department":[{"_id":"LaEr"}],"publication":"Electronic Communications in Probability","page":"1-13","status":"public","language":[{"iso":"eng"}],"publication_status":"published","author":[{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"}],"title":"Dynamics of a rank-one perturbation of a Hermitian matrix","intvolume":"        28","article_processing_charge":"No","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.","volume":28,"date_published":"2023-02-08T00:00:00Z","fulldoi":"https://doi.org/10.1214/23-ECP516","has_accepted_license":"1","abstract":[{"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.","lang":"eng"}],"day":"08","quality_controlled":"1","_id":"12683","doi":"10.1214/23-ECP516","file_date_updated":"2023-02-27T09:43:27Z","publisher":"Institute of Mathematical Statistics"}]