[{"publication_status":"published","corr_author":"1","publication":"Journal of Functional Analysis","external_id":{"isi":["001325502400001"]},"day":"15","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"volume":287,"ec_funded":1,"intvolume":"       287","publisher":"Elsevier","isi":1,"article_processing_charge":"Yes (via OA deal)","type":"journal_article","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_type":"hybrid","date_published":"2024-08-15T00:00:00Z","quality_controlled":"1","date_updated":"2026-04-07T12:37:11Z","_id":"17049","month":"08","doi":"10.1016/j.jfa.2024.110495","ddc":["510"],"issue":"4","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (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.","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>","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>.","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>","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."},"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"file":[{"relation":"main_file","date_updated":"2025-06-24T13:14:21Z","file_size":1374854,"checksum":"07d3f73e0c56e68eb110851842c22ee0","access_level":"open_access","date_created":"2025-06-24T13:14:21Z","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","content_type":"application/pdf","success":1,"file_id":"19891","creator":"dernst"}],"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_created":"2024-05-26T22:00:57Z","file_date_updated":"2025-06-24T13:14:21Z","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"}],"acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","department":[{"_id":"LaEr"}],"has_accepted_license":"1","OA_place":"publisher","article_number":"110495","year":"2024","scopus_import":"1","oa_version":"Published Version","oa":1},{"year":"2024","OA_place":"repository","oa":1,"oa_version":"Preprint","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"}],"citation":{"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>.","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>","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.).","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>.","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>","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. ."},"title":"Eigenstate thermalisation at the edge for Wigner matrices","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"date_created":"2025-04-11T08:19:22Z","abstract":[{"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.","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2024-12-17T00:00:00Z","type":"preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.05488"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","article_processing_charge":"No","arxiv":1,"doi":"10.48550/arXiv.2309.05488","month":"12","date_updated":"2026-04-07T12:37:11Z","_id":"19545","language":[{"iso":"eng"}],"day":"17","corr_author":"1","publication":"arXiv","external_id":{"arxiv":["2309.05488"]},"publication_status":"draft","ec_funded":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]}},{"article_processing_charge":"No","date_published":"2024-10-14T00:00:00Z","year":"2024","type":"preprint","OA_place":"repository","status":"public","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10809","open_access":"1"}],"oa_version":"Preprint","date_updated":"2026-04-07T12:37:11Z","_id":"19551","arxiv":1,"oa":1,"month":"10","doi":"10.48550/arXiv.2410.10809","corr_author":"1","external_id":{"arxiv":["2410.10809"]},"publication":"arXiv","citation":{"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>.","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>.","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>","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>.","short":"S.J. Henheik, T. Wessel, ArXiv (n.d.).","ieee":"S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” <i>arXiv</i>. .","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>"},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"first_name":"Tom","last_name":"Wessel","full_name":"Wessel, Tom"}],"title":"Response theory for locally gapped systems","publication_status":"draft","language":[{"iso":"eng"}],"day":"14","date_created":"2025-04-11T11:54:56Z","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."}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"department":[{"_id":"LaEr"}]},{"language":[{"iso":"eng"}],"day":"21","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"first_name":"Edwin","full_name":"Langmann, Edwin","last_name":"Langmann"},{"last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"}],"publication":"arXiv","external_id":{"arxiv":["2409.17297"]},"citation":{"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>","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>arXiv</i>. .","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>.","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","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>","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>.","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>."},"corr_author":"1","title":"Multi-band superconductors have enhanced critical temperatures","publication_status":"draft","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"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"}],"date_created":"2025-04-11T11:43:58Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2024-10-21T00:00:00Z","year":"2024","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.17297"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","type":"preprint","OA_place":"repository","article_processing_charge":"No","arxiv":1,"oa":1,"doi":"10.48550/arXiv.2409.17297","month":"10","oa_version":"Preprint","_id":"19550","date_updated":"2026-04-07T12:37:11Z"},{"title":"Cusp universality for correlated random matrices","citation":{"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>","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>.","short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","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>.","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>","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>."},"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr","last_name":"Riabov","full_name":"Riabov, Volodymyr"}],"acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","department":[{"_id":"LaEr"}],"date_created":"2025-04-11T08:48:21Z","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."}],"OA_place":"repository","year":"2024","oa":1,"oa_version":"Preprint","day":"03","language":[{"iso":"eng"}],"publication_status":"draft","corr_author":"1","publication":"arXiv","external_id":{"arxiv":["2410.06813"]},"ec_funded":1,"related_material":{"record":[{"relation":"later_version","status":"public","id":"20322"},{"status":"public","id":"20575","relation":"dissertation_contains"},{"relation":"dissertation_contains","id":"19540","status":"public"}]},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"preprint","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.06813"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2024-11-03T00:00:00Z","article_processing_charge":"No","doi":"10.48550/arXiv.2410.06813","month":"11","arxiv":1,"date_updated":"2026-04-07T12:37:11Z","_id":"19547"},{"article_processing_charge":"Yes (in subscription journal)","OA_type":"hybrid","date_published":"2024-10-01T00:00:00Z","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-04-07T13:01:40Z","quality_controlled":"1","_id":"14542","arxiv":1,"ddc":["510"],"issue":"9","month":"10","doi":"10.1142/s0129055x2360005x","corr_author":"1","publication":"Reviews in Mathematical Physics","external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"publication_status":"published","language":[{"iso":"eng"}],"day":"01","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"volume":36,"related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"},{"relation":"dissertation_contains","status":"public","id":"18135"}]},"isi":1,"publisher":"World Scientific Publishing","intvolume":"        36","ec_funded":1,"has_accepted_license":"1","year":"2024","OA_place":"publisher","article_number":"2360005 ","oa_version":"Published Version","scopus_import":"1","oa":1,"citation":{"ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","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>","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>.","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>.","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>","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."},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard"},{"full_name":"Roos, Barbara","last_name":"Roos","orcid":"0000-0002-9071-5880","first_name":"Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425"}],"title":"Universality in low-dimensional BCS theory","file":[{"success":1,"file_id":"18786","creator":"dernst","content_type":"application/pdf","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","date_updated":"2025-01-09T07:56:28Z","relation":"main_file","access_level":"open_access","checksum":"2b053a4223b4db14b90520999ec56054","date_created":"2025-01-09T07:56:28Z","file_size":503910}],"article_type":"original","date_created":"2023-11-15T23:48:14Z","file_date_updated":"2025-01-09T07:56:28Z","abstract":[{"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.","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"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.","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}]},{"publisher":"Institute of Science and Technology Austria","ec_funded":1,"keyword":["Random Matrices","Spectrum","Central Limit Theorem","Resolvent","Free Probability"],"related_material":{"record":[{"relation":"part_of_dissertation","id":"17173","status":"public"},{"id":"11135","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"17047","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"17154","status":"public"},{"status":"public","id":"17174","relation":"part_of_dissertation"}]},"supervisor":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"}],"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"]},"day":"26","language":[{"iso":"eng"}],"publication_status":"published","corr_author":"1","degree_awarded":"PhD","month":"06","doi":"10.15479/at:ista:17164","ddc":["519"],"date_updated":"2026-04-07T13:02:13Z","_id":"17164","type":"dissertation","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","status":"public","date_published":"2024-06-26T00:00:00Z","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","page":"206","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png"},"date_created":"2024-06-24T11:23:29Z","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2024-06-26T12:44:53Z","file":[{"creator":"jreker","file_id":"17176","content_type":"application/pdf","file_name":"ISTA_Thesis_JReker.pdf","date_updated":"2024-06-26T12:44:53Z","relation":"main_file","file_size":2783027,"access_level":"open_access","date_created":"2024-06-26T12:39:36Z","checksum":"fb16d86e1f2753dc3a9e14d2bdfd84cd"},{"content_type":"application/zip","creator":"jreker","file_id":"17177","date_updated":"2024-06-26T12:44:53Z","relation":"source_file","file_size":3054878,"checksum":"cb1e54009d47c1dcf5b866c4566fa27f","access_level":"closed","date_created":"2024-06-26T12:39:42Z","file_name":"ISTA_Thesis_JReker_SourceFiles.zip"}],"title":"Central limit theorems for random matrices: From resolvents to free probability","citation":{"ieee":"J. Reker, “Central limit theorems for random matrices: From resolvents to free probability,” Institute of Science and Technology Austria, 2024.","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>.","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>","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>.","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."},"author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","last_name":"Reker","full_name":"Reker, Jana"}],"oa":1,"oa_version":"Published Version","OA_place":"publisher","year":"2024","has_accepted_license":"1"},{"publication":"Mathematical Physics, Analysis and Geometry","external_id":{"arxiv":["2307.11029"],"isi":["001251464300001"]},"publication_status":"published","language":[{"iso":"eng"}],"day":"20","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"volume":27,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"17164"}]},"isi":1,"publisher":"Springer Nature","ec_funded":1,"intvolume":"        27","article_processing_charge":"Yes (via OA deal)","date_published":"2024-06-20T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","type":"journal_article","_id":"17154","date_updated":"2026-04-07T13:02:12Z","quality_controlled":"1","issue":"3","ddc":["519"],"arxiv":1,"doi":"10.1007/s11040-024-09483-y","month":"06","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>","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.","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>.","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).","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.” <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>."},"author":[{"first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","full_name":"Reker, Jana"}],"title":"Fluctuation moments for regular functions of Wigner Matrices","article_type":"original","file":[{"file_name":"2024_MathPhysAnaGeo_Reker.pdf","relation":"main_file","date_updated":"2024-06-26T11:26:42Z","file_size":1327596,"date_created":"2024-06-26T11:26:42Z","checksum":"7d04318d66f765621bdcb648378d458e","access_level":"open_access","success":1,"file_id":"17175","creator":"cchlebak","content_type":"application/pdf"}],"file_date_updated":"2024-06-26T11:26:42Z","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."}],"date_created":"2024-06-21T09:31:17Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"department":[{"_id":"LaEr"}],"has_accepted_license":"1","year":"2024","article_number":"10","oa_version":"Published Version","scopus_import":"1","oa":1},{"_id":"17047","date_updated":"2026-04-07T13:02:12Z","quality_controlled":"1","issue":"2","arxiv":1,"doi":"10.1142/s2010326324500072","month":"04","article_processing_charge":"No","date_published":"2024-04-01T00:00:00Z","OA_type":"green","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2212.14638","open_access":"1"}],"type":"journal_article","volume":13,"publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"related_material":{"record":[{"id":"17164","status":"public","relation":"dissertation_contains"}]},"isi":1,"publisher":"World Scientific Publishing","intvolume":"        13","ec_funded":1,"publication":"Random Matrices: Theory and Applications","external_id":{"arxiv":["2212.14638"],"isi":["001229295200002"]},"corr_author":"1","publication_status":"published","language":[{"iso":"eng"}],"day":"01","oa_version":"Preprint","scopus_import":"1","oa":1,"year":"2024","article_number":"2450007","OA_place":"repository","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"}],"date_created":"2024-05-23T08:31:57Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"author":[{"last_name":"Dubach","full_name":"Dubach, Guillaume","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137"},{"full_name":"Reker, Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana"}],"citation":{"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.","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>.","short":"G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (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.","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>.","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>"},"title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix","article_type":"original"},{"date_published":"2023-04-01T00:00:00Z","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","arxiv":1,"ddc":["510"],"doi":"10.1007/s00440-022-01156-7","month":"04","date_updated":"2024-10-09T21:03:02Z","quality_controlled":"1","_id":"11741","language":[{"iso":"eng"}],"day":"01","corr_author":"1","publication":"Probability Theory and Related Fields","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"publication_status":"published","isi":1,"publisher":"Springer Nature","intvolume":"       185","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"volume":185,"year":"2023","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","file":[{"success":1,"creator":"dernst","file_id":"14054","content_type":"application/pdf","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","relation":"main_file","date_updated":"2023-08-14T12:47:32Z","access_level":"open_access","checksum":"b9247827dae5544d1d19c37abe547abc","date_created":"2023-08-14T12:47:32Z","file_size":782278}],"article_type":"original","citation":{"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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","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.","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>"},"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"title":"Quenched universality for deformed Wigner matrices","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).","department":[{"_id":"LaEr"}],"page":"1183–1218","date_created":"2022-08-07T22:02:00Z","file_date_updated":"2023-08-14T12:47:32Z","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."}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}},{"oa_version":"Preprint","scopus_import":"1","oa":1,"year":"2023","date_created":"2023-12-10T23:01:00Z","abstract":[{"text":"For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. ","lang":"eng"},{"text":"On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.","lang":"fre"}],"acknowledgement":"The first author was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated editor for carefully reading this paper and providing helpful comments that improved the quality of the article. Also the authors would like to thank Peter Forrester for pointing out the reference [12] that was absent in the previous version of the manuscript.","department":[{"_id":"LaEr"}],"page":"2083-2105","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"citation":{"ieee":"L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.","apa":"Erdös, L., &#38; Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>","mla":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:<a href=\"https://doi.org/10.1214/22-AIHP1304\">10.1214/22-AIHP1304</a>.","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105.","ista":"Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.","ama":"Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2023;59(4):2083-2105. doi:<a href=\"https://doi.org/10.1214/22-AIHP1304\">10.1214/22-AIHP1304</a>","chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>."},"title":"Functional CLT for non-Hermitian random matrices","article_type":"original","date_updated":"2025-09-09T13:41:08Z","quality_controlled":"1","_id":"14667","arxiv":1,"issue":"4","doi":"10.1214/22-AIHP1304","month":"11","article_processing_charge":"No","date_published":"2023-11-01T00:00:00Z","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.11382","open_access":"1"}],"status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"volume":59,"publication_identifier":{"issn":["0246-0203"]},"isi":1,"intvolume":"        59","publisher":"Institute of Mathematical Statistics","ec_funded":1,"corr_author":"1","external_id":{"isi":["001098456400010"],"arxiv":["2112.11382"]},"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","publication_status":"published","language":[{"iso":"eng"}],"day":"01"},{"article_type":"original","file":[{"date_updated":"2023-02-27T09:43:27Z","relation":"main_file","access_level":"open_access","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","date_created":"2023-02-27T09:43:27Z","file_size":479105,"file_name":"2023_ElectCommProbability_Dubach.pdf","content_type":"application/pdf","success":1,"creator":"dernst","file_id":"12692"}],"author":[{"orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","full_name":"Dubach, Guillaume","last_name":"Dubach"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"}],"citation":{"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.","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>.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","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>","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>."},"title":"Dynamics of a rank-one perturbation of a Hermitian matrix","department":[{"_id":"LaEr"}],"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.","page":"1-13","file_date_updated":"2023-02-27T09:43:27Z","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"}],"date_created":"2023-02-26T23:01:01Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2023","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"day":"08","external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"publication":"Electronic Communications in Probability","corr_author":"1","publication_status":"published","isi":1,"publisher":"Institute of Mathematical Statistics","intvolume":"        28","ec_funded":1,"publication_identifier":{"eissn":["1083-589X"]},"volume":28,"project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"date_published":"2023-02-08T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_processing_charge":"No","ddc":["510"],"arxiv":1,"doi":"10.1214/23-ECP516","month":"02","_id":"12683","date_updated":"2025-04-14T07:44:00Z","quality_controlled":"1"},{"article_type":"original","citation":{"mla":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>.","ama":"Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. 2023;29(2):1063-1079. doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>","chicago":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2023. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>.","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","ieee":"L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” <i>Bernoulli</i>, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.","apa":"Erdös, L., &#38; Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>"},"author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","department":[{"_id":"LaEr"}],"page":"1063-1079","abstract":[{"text":"We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.","lang":"eng"}],"date_created":"2023-03-05T23:01:05Z","year":"2023","oa":1,"oa_version":"Preprint","scopus_import":"1","language":[{"iso":"eng"}],"day":"01","publication":"Bernoulli","external_id":{"isi":["000947270100008"],"arxiv":["2112.12093 "]},"corr_author":"1","publication_status":"published","isi":1,"ec_funded":1,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","intvolume":"        29","publication_identifier":{"issn":["1350-7265"]},"volume":29,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"date_published":"2023-05-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","article_processing_charge":"No","issue":"2","arxiv":1,"month":"05","doi":"10.3150/22-BEJ1490","_id":"12707","quality_controlled":"1","date_updated":"2025-04-14T07:57:19Z"},{"language":[{"iso":"eng"}],"day":"01","corr_author":"1","external_id":{"isi":["000946432400015"],"arxiv":["2012.13218"]},"publication":"Annals of Applied Probability","publication_status":"published","isi":1,"publisher":"Institute of Mathematical Statistics","ec_funded":1,"intvolume":"        33","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"issn":["1050-5164"]},"volume":33,"date_published":"2023-02-01T00:00:00Z","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.13218"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","article_processing_charge":"No","arxiv":1,"issue":"1","doi":"10.1214/22-AAP1820","month":"02","date_updated":"2025-04-14T07:57:19Z","quality_controlled":"1","_id":"12761","article_type":"original","citation":{"mla":"Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. 2023;33(1):447-489. doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” <i>Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>"},"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"title":"Functional central limit theorems for Wigner matrices","acknowledgement":"The second author is partially funded by the ERC Advanced Grant “RMTBEYOND” No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","department":[{"_id":"LaEr"}],"page":"447-489","date_created":"2023-03-26T22:01:08Z","abstract":[{"text":"We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"year":"2023","oa":1,"oa_version":"Preprint","scopus_import":"1"},{"ddc":["510"],"month":"07","doi":"10.1007/s00220-023-04692-y","_id":"12792","date_updated":"2025-04-14T07:57:19Z","quality_controlled":"1","date_published":"2023-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","article_processing_charge":"Yes (via OA deal)","isi":1,"intvolume":"       401","publisher":"Springer Nature","ec_funded":1,"volume":401,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"language":[{"iso":"eng"}],"day":"01","external_id":{"isi":["000957343500001"]},"publication":"Communications in Mathematical Physics","corr_author":"1","publication_status":"published","oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2023","has_accepted_license":"1","department":[{"_id":"LaEr"}],"acknowledgement":"We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","page":"1665-1700","file_date_updated":"2023-10-04T12:09:18Z","abstract":[{"text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics.","lang":"eng"}],"date_created":"2023-04-02T22:01:11Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","file":[{"content_type":"application/pdf","success":1,"file_id":"14397","creator":"dernst","date_updated":"2023-10-04T12:09:18Z","relation":"main_file","file_size":859967,"date_created":"2023-10-04T12:09:18Z","checksum":"72057940f76654050ca84a221f21786c","access_level":"open_access","file_name":"2023_CommMathPhysics_Cipolloni.pdf"}],"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. 2023;401:1665-1700. doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” <i>Communications in Mathematical Physics</i>, vol. 401. Springer Nature, pp. 1665–1700, 2023."},"title":"On the spectral form factor for random matrices"},{"article_processing_charge":"No","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2010.16083","open_access":"1"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","date_published":"2023-08-01T00:00:00Z","date_updated":"2025-09-09T14:12:00Z","quality_controlled":"1","_id":"14750","doi":"10.1214/22-aap1882","month":"08","arxiv":1,"issue":"4","publication_status":"published","corr_author":"1","publication":"The Annals of Applied Probability","external_id":{"isi":["001031710500012"],"arxiv":["2010.16083"]},"day":"01","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"issn":["1050-5164"]},"volume":33,"intvolume":"        33","ec_funded":1,"publisher":"Institute of Mathematical Statistics","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"isi":1,"year":"2023","scopus_import":"1","oa_version":"Preprint","oa":1,"title":"Local laws for multiplication of random matrices","author":[{"first_name":"Xiucai","last_name":"Ding","full_name":"Ding, Xiucai"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang","last_name":"Ji","full_name":"Ji, Hong Chang"}],"citation":{"mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>.","ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. 2023;33(4):2981-3009. doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>.","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009.","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","apa":"Ding, X., &#38; Ji, H. C. (2023). Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>"},"article_type":"original","date_created":"2024-01-08T13:03:18Z","abstract":[{"lang":"eng","text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. "}],"page":"2981-3009","acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","department":[{"_id":"LaEr"}]},{"type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.02728","open_access":"1"}],"date_published":"2023-02-01T00:00:00Z","article_processing_charge":"No","month":"02","doi":"10.1214/22-aap1826","arxiv":1,"issue":"1","quality_controlled":"1","date_updated":"2025-04-14T07:57:19Z","_id":"14775","day":"01","language":[{"iso":"eng"}],"publication_status":"published","corr_author":"1","external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]},"publication":"The Annals of Applied Probability","publisher":"Institute of Mathematical Statistics","intvolume":"        33","ec_funded":1,"isi":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"publication_identifier":{"issn":["1050-5164"]},"volume":33,"year":"2023","oa":1,"scopus_import":"1","oa_version":"Preprint","article_type":"original","title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","citation":{"mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. 2023;33(1):677-725. doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>","ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","apa":"Schnelli, K., &#38; Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>"},"author":[{"orcid":"0000-0003-0954-3231","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","last_name":"Schnelli"},{"orcid":"0000-0003-1559-1205","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"page":"677-725","acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"date_created":"2024-01-10T09:23:31Z","abstract":[{"lang":"eng","text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble."}]},{"oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2023","has_accepted_license":"1","department":[{"_id":"LaEr"}],"acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","page":"25-60","abstract":[{"lang":"eng","text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix."}],"file_date_updated":"2024-01-16T08:47:31Z","date_created":"2024-01-10T09:29:25Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","file":[{"file_name":"2023_StochasticProcAppl_Ding.pdf","date_updated":"2024-01-16T08:47:31Z","relation":"main_file","access_level":"open_access","checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","date_created":"2024-01-16T08:47:31Z","file_size":1870349,"success":1,"creator":"dernst","file_id":"14806","content_type":"application/pdf"}],"citation":{"mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol. 163, Elsevier, 2023, pp. 25–60, doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>.","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier, pp. 25–60, 2023.","apa":"Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>"},"author":[{"first_name":"Xiucai","full_name":"Ding, Xiucai","last_name":"Ding"},{"full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"title":"Spiked multiplicative random matrices and principal components","ddc":["510"],"arxiv":1,"month":"09","doi":"10.1016/j.spa.2023.05.009","_id":"14780","quality_controlled":"1","date_updated":"2025-07-16T08:01:03Z","date_published":"2023-09-01T00:00:00Z","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_processing_charge":"Yes (in subscription journal)","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"isi":1,"publisher":"Elsevier","ec_funded":1,"intvolume":"       163","publication_identifier":{"eissn":["1879-209X"],"issn":["0304-4149"]},"volume":163,"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"language":[{"iso":"eng"}],"day":"01","publication":"Stochastic Processes and their Applications","external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"publication_status":"published"},{"article_processing_charge":"No","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","date_published":"2023-11-01T00:00:00Z","_id":"14849","date_updated":"2025-09-09T14:23:34Z","quality_controlled":"1","month":"11","doi":"10.1214/23-aop1643","issue":"6","arxiv":1,"publication_status":"published","external_id":{"isi":["001112165000004"],"arxiv":["2206.04448"]},"publication":"The Annals of Probability","corr_author":"1","day":"01","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0091-1798"]},"volume":51,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"ec_funded":1,"publisher":"Institute of Mathematical Statistics","intvolume":"        51","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"isi":1,"year":"2023","scopus_import":"1","oa_version":"Preprint","oa":1,"title":"On the rightmost eigenvalue of non-Hermitian random matrices","citation":{"mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>"},"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder"},{"first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"article_type":"original","abstract":[{"lang":"eng","text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal."}],"date_created":"2024-01-22T08:08:41Z","page":"2192-2242","department":[{"_id":"LaEr"}],"acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation."},{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020"}],"volume":76,"publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"intvolume":"        76","publisher":"Wiley","ec_funded":1,"isi":1,"publication_status":"published","corr_author":"1","external_id":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"publication":"Communications on Pure and Applied Mathematics","day":"01","language":[{"iso":"eng"}],"date_updated":"2025-03-31T16:00:54Z","quality_controlled":"1","_id":"10405","month":"05","doi":"10.1002/cpa.22028","arxiv":1,"issue":"5","ddc":["510"],"article_processing_charge":"Yes (via OA deal)","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2023-05-01T00:00:00Z","tmp":{"short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"date_created":"2021-12-05T23:01:41Z","file_date_updated":"2023-10-04T09:21:48Z","abstract":[{"lang":"eng","text":"We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. "}],"page":"946-1034","acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","department":[{"_id":"LaEr"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>"},"file":[{"content_type":"application/pdf","success":1,"creator":"dernst","file_id":"14388","relation":"main_file","date_updated":"2023-10-04T09:21:48Z","date_created":"2023-10-04T09:21:48Z","checksum":"8346bc2642afb4ccb7f38979f41df5d9","access_level":"open_access","file_size":803440,"file_name":"2023_CommPureMathematics_Cipolloni.pdf"}],"article_type":"original","scopus_import":"1","oa_version":"Published Version","oa":1,"has_accepted_license":"1","year":"2023"}]