[{"oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2025","article_number":"253","OA_place":"publisher","has_accepted_license":"1","department":[{"_id":"LaEr"}],"license":"https://creativecommons.org/licenses/by/4.0/","acknowledgement":"We thank Giorgio Cipolloni for many productive discussions and the anonymous referees for several useful suggestions and spotting some typos. Open access funding provided by Institute of Science and Technology (IST Austria).","file_date_updated":"2025-09-10T07:48:21Z","abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the Zigzag strategy, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.","lang":"eng"}],"date_created":"2025-09-10T05:38:17Z","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)"},"article_type":"original","file":[{"success":1,"file_id":"20336","creator":"dernst","content_type":"application/pdf","file_name":"2025_CommMathPhysics_Erdoes.pdf","relation":"main_file","date_updated":"2025-09-10T07:48:21Z","file_size":1465827,"checksum":"abd32af7b8ca6dc5b9080823a433986b","date_created":"2025-09-10T07:48:21Z","access_level":"open_access"}],"PlanS_conform":"1","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"full_name":"Riabov, Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"}],"citation":{"ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” Communications in Mathematical Physics, vol. 406, no. 10. Springer Nature, 2025.","apa":"Erdös, L., Henheik, S. J., & Riabov, V. (2025). Cusp universality for correlated random matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-025-05417-z","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” Communications in Mathematical Physics, vol. 406, no. 10, 253, Springer Nature, 2025, doi:10.1007/s00220-025-05417-z.","ista":"Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253.","short":"L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025).","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 2025;406(10). doi:10.1007/s00220-025-05417-z","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” Communications in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s00220-025-05417-z."},"title":"Cusp universality for correlated random matrices","ddc":["510"],"issue":"10","arxiv":1,"doi":"10.1007/s00220-025-05417-z","month":"09","_id":"20322","quality_controlled":"1","date_updated":"2026-04-07T12:32:19Z","date_published":"2025-09-01T00:00:00Z","OA_type":"hybrid","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","type":"journal_article","article_processing_charge":"Yes (via OA deal)","isi":1,"publisher":"Springer Nature","intvolume":" 406","volume":406,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"related_material":{"record":[{"id":"19547","status":"public","relation":"earlier_version"},{"relation":"dissertation_contains","id":"20575","status":"public"}]},"language":[{"iso":"eng"}],"day":"01","publication":"Communications in Mathematical Physics","external_id":{"arxiv":["2410.06813"],"isi":["001565019000005"]},"corr_author":"1","publication_status":"published"},{"date_updated":"2026-04-07T12:32:19Z","_id":"20576","oa_version":"Preprint","month":"06","doi":"10.48550/ARXIV.2506.06441","oa":1,"article_processing_charge":"No","OA_place":"repository","type":"preprint","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2506.06441"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2025-06-06T00:00:00Z","year":"2025","related_material":{"record":[{"status":"public","id":"20575","relation":"dissertation_contains"}]},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"date_created":"2025-10-29T19:09:03Z","abstract":[{"text":"We prove that a very general class of $N\\times N$ Hermitian random band matrices is in the delocalized phase when the band width $W$ exceeds the critical threshold, $W\\gg \\sqrt{N}$. In this regime, we show that, in the bulk spectrum, the eigenfunctions are fully delocalized, the eigenvalues follow the universal Wigner-Dyson statistics, and quantum unique ergodicity holds for general diagonal observables with an optimal convergence rate. Our results are valid for general variance profiles, arbitrary single entry distributions, in both real-symmetric and complex-Hermitian symmetry classes. In particular, our work substantially generalizes the recent breakthrough result of Yau and Yin [arXiv:2501.01718], obtained for a specific complex Hermitian Gaussian block band matrix. The main technical input is the optimal multi-resolvent local laws -- both in the averaged and fully isotropic form. We also generalize the $\\sqrtη$-rule from [arXiv:2012.13215] to exploit the additional effect of traceless observables. Our analysis is based on the zigzag strategy, complemented with a new global-scale estimate derived using the static version of the master inequalities, while the zig-step and the a priori estimates on the deterministic approximations are proven dynamically.","lang":"eng"}],"ec_funded":1,"acknowledgement":" Supported by the ERC\r\nAdvanced Grant ”RMTBeyond” No. 101020331.","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publication_status":"draft","title":"The zigzag strategy for random band matrices","corr_author":"1","publication":"arXiv","citation":{"mla":"Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” ArXiv, doi:10.48550/ARXIV.2506.06441.","short":"L. Erdös, V. Riabov, ArXiv (n.d.).","ista":"Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv, 10.48550/ARXIV.2506.06441.","chicago":"Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2506.06441.","ama":"Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv. doi:10.48550/ARXIV.2506.06441","ieee":"L. Erdös and V. Riabov, “The zigzag strategy for random band matrices,” arXiv. .","apa":"Erdös, L., & Riabov, V. (n.d.). The zigzag strategy for random band matrices. arXiv. https://doi.org/10.48550/ARXIV.2506.06441"},"author":[{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Riabov, Volodymyr","last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"day":"06","language":[{"iso":"eng"}]},{"author":[{"last_name":"Riabov","full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"}],"citation":{"chicago":"Riabov, Volodymyr. “Universality in Random Matrices with Spatial Structure.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20575.","ama":"Riabov V. Universality in random matrices with spatial structure. 2025. doi:10.15479/AT-ISTA-20575","ista":"Riabov V. 2025. Universality in random matrices with spatial structure. Institute of Science and Technology Austria.","short":"V. Riabov, Universality in Random Matrices with Spatial Structure, Institute of Science and Technology Austria, 2025.","mla":"Riabov, Volodymyr. Universality in Random Matrices with Spatial Structure. Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-20575.","apa":"Riabov, V. (2025). Universality in random matrices with spatial structure. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-20575","ieee":"V. Riabov, “Universality in random matrices with spatial structure,” Institute of Science and Technology Austria, 2025."},"title":"Universality in random matrices with spatial structure","file":[{"success":1,"creator":"vriabov","file_id":"20577","content_type":"application/pdf","file_name":"riabov_thesis-pdfa.pdf","relation":"main_file","date_updated":"2025-10-29T18:53:59Z","date_created":"2025-10-29T18:53:59Z","access_level":"open_access","checksum":"6a0487b2b66bb35d44b394756d44b8b4","file_size":7536583},{"creator":"vriabov","file_id":"20578","content_type":"application/x-zip-compressed","file_name":"manuscript.zip","checksum":"224efda6bf9864d296a1e5e0124c1e8f","date_created":"2025-10-29T18:54:53Z","access_level":"closed","file_size":17841612,"date_updated":"2025-10-29T18:54:53Z","relation":"source_file"}],"abstract":[{"text":"This thesis deals with eigenvalue and eigenvector universality results for random matrix ensembles equipped with non-trivial spatial structure. We consider both mean-field models with a general variance profile (Wigner-type matrices) and correlation structure (correlated matrices) among the entries, as well as non-mean-field random band matrices with bandwidth W >> N^(1/2).\r\n\r\nTo extract the universal properties of random matrix spectra and eigenvectors, we obtain concentration estimates for their resolvent, the local laws, which generalize the celebrated Wigner semicircle law for a broad class of random matrices to much finer spectral scales. The local laws hold for both a single resolvent as well as for products of multiple resolvents, known as resolvent chains, and express the remarkable approximately-deterministic behavior of these objects down to the microscopic scale.\r\n\r\nOur primary tool for establishing the local laws is the dynamical Zigzag strategy, which we develop in the setting of spatially-inhomogeneous random matrices. Our proof method systematically addresses the challenges arising from non-trivial spatial structures and is robust to all types of singularities in the spectrum, as we demonstrate in the correlated setting. Furthermore, we incorporate the analysis of the deterministic resolvent chain approximations into the dynamical framework of the Zigzag strategy, synthesizing a unified toolkit for establishing multi-resolvent local laws.\r\n\r\nUsing these methods, we prove complete eigenvector delocalization, the Eigenstate Thermalization Hypothesis, and Wigner-Dyson universality in the bulk for random band matrices down to the optimal bandwidth W >> N^(1/2). For mean-field ensembles, we establish universality of local eigenvalue statistics at the cups for random matrices with correlated entries, and the Eigenstate Thermalization Hypothesis for Wigner-type matrices in the bulk of the spectrum.\r\n\r\nFinally, this thesis also contains other applications of the multi-resolvent local laws to spatially-inhomogeneous random matrices, obtained prior to the development of the Zigzag strategy. In particular, we provide a complete analysis of mesoscopic linear-eigenvalue statistics of Wigner-type matrices in all spectral regimes, including the novel cusps, and rigorously establish the prethermalization phenomenon for deformed Wigner matrices.\r\n\r\nThe main body of this thesis consists of seven research papers (listed on page xi), each presented in a separate chapter with its own introduction and all relevant context, suitable to be read independently. We ask the reader’s indulgence for the repetitions in the historical overviews and other minor redundancies that remain among the chapters as a result. The overall Introduction, preceding the chapters, provides a condensed, informal summary of the main ideas and concepts at the core of these works.\r\n","lang":"eng"}],"file_date_updated":"2025-10-29T18:54:53Z","date_created":"2025-10-29T19:12:24Z","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":"GradSch"},{"_id":"LaEr"}],"acknowledgement":"The work comprising this thesis was supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo.101020331 awarded to my advisor.","page":"436","has_accepted_license":"1","year":"2025","OA_place":"publisher","oa_version":"Published Version","oa":1,"degree_awarded":"PhD","corr_author":"1","publication_status":"published","language":[{"iso":"eng"}],"day":"3","publication_identifier":{"isbn":["978-3-99078-064-0"],"issn":["2663-337X"]},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"related_material":{"record":[{"status":"public","id":"20322","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"18764"},{"id":"13317","status":"public","relation":"part_of_dissertation"},{"status":"deleted","id":"19368","relation":"part_of_dissertation"},{"status":"public","id":"18554","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"20576","status":"public"},{"relation":"part_of_dissertation","id":"17174","status":"public"},{"id":"19547","status":"public","relation":"part_of_dissertation"},{"id":"19598","status":"public","relation":"part_of_dissertation"}]},"supervisor":[{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"}],"ec_funded":1,"publisher":"Institute of Science and Technology Austria","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","date_published":"2025-11-03T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","status":"public","type":"dissertation","_id":"20575","date_updated":"2026-04-07T12:32:20Z","ddc":["515","519"],"month":"11","doi":"10.15479/AT-ISTA-20575"},{"article_type":"original","file":[{"file_name":"2025_ProbTheoryRelatFields_Riabov.pdf","date_updated":"2025-12-30T13:10:05Z","relation":"main_file","checksum":"700229b280725c0d6aad0d71362cce5f","date_created":"2025-12-30T13:10:05Z","access_level":"open_access","file_size":919213,"success":1,"file_id":"20916","creator":"dernst","content_type":"application/pdf"}],"PlanS_conform":"1","citation":{"mla":"Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” Probability Theory and Related Fields, vol. 193, Springer Nature, 2025, pp. 1183–237, doi:10.1007/s00440-025-01373-w.","short":"V. Riabov, Probability Theory and Related Fields 193 (2025) 1183–1237.","ista":"Riabov V. 2025. Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. 193, 1183–1237.","chicago":"Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” Probability Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01373-w.","ama":"Riabov V. Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. 2025;193:1183-1237. doi:10.1007/s00440-025-01373-w","ieee":"V. Riabov, “Linear Eigenvalue statistics at the cusp,” Probability Theory and Related Fields, vol. 193. Springer Nature, pp. 1183–1237, 2025.","apa":"Riabov, V. (2025). Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01373-w"},"author":[{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov"}],"title":"Linear Eigenvalue statistics at the cusp","department":[{"_id":"LaEr"}],"acknowledgement":"I would like to express my gratitude to László Erdős for his careful guidance and supervision of my work. I am also thankful to Jana Reker and Joscha Henheik for many helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria).","page":"1183-1237","abstract":[{"lang":"eng","text":"We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes."}],"file_date_updated":"2025-12-30T13:10:05Z","date_created":"2025-04-20T22:01:28Z","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":"2025","OA_place":"publisher","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"day":"01","external_id":{"arxiv":["2307.07432"],"isi":["001466997300001"]},"publication":"Probability Theory and Related Fields","corr_author":"1","publication_status":"published","isi":1,"intvolume":" 193","publisher":"Springer Nature","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"volume":193,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"20575"}]},"date_published":"2025-12-01T00:00:00Z","OA_type":"hybrid","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"arxiv":1,"doi":"10.1007/s00440-025-01373-w","month":"12","_id":"19598","quality_controlled":"1","date_updated":"2026-04-07T12:32:19Z"},{"page":"467-503","acknowledgement":"I am very grateful to Vadim Kaloshin for suggesting the topic, his guidance during this project, and many helpful comments on an earlier version of the manuscript. Moreover, I would like to thank Comlan Edmond Koudjinan and Volodymyr Riabov for interesting discussions. Partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331 is gratefully acknowledged. This project received funding from the European Research Council (ERC) ERC Grant No. 885707.","department":[{"_id":"LaEr"}],"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":"2024-09-22T22:01:43Z","abstract":[{"text":"It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus.","lang":"eng"}],"file_date_updated":"2025-01-13T08:51:40Z","file":[{"content_type":"application/pdf","success":1,"file_id":"18828","creator":"dernst","relation":"main_file","date_updated":"2025-01-13T08:51:40Z","access_level":"open_access","checksum":"650fe115d998fe0ac3a8d0c7519447c8","date_created":"2025-01-13T08:51:40Z","file_size":659100,"file_name":"2025_ErgodicTheory_Henheik.pdf"}],"article_type":"original","title":"Deformational rigidity of integrable metrics on the torus","citation":{"mla":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” Ergodic Theory and Dynamical Systems, vol. 45, no. 2, Cambridge University Press, 2025, pp. 467–503, doi:10.1017/etds.2024.48.","chicago":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2025. https://doi.org/10.1017/etds.2024.48.","ama":"Henheik SJ. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 2025;45(2):467-503. doi:10.1017/etds.2024.48","short":"S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503.","ista":"Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 45(2), 467–503.","ieee":"S. J. Henheik, “Deformational rigidity of integrable metrics on the torus,” Ergodic Theory and Dynamical Systems, vol. 45, no. 2. Cambridge University Press, pp. 467–503, 2025.","apa":"Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2024.48"},"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"}],"oa":1,"scopus_import":"1","oa_version":"Published Version","OA_place":"publisher","year":"2025","has_accepted_license":"1","intvolume":" 45","publisher":"Cambridge University Press","ec_funded":1,"isi":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"},{"grant_number":"885707","call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"volume":45,"publication_identifier":{"issn":["0143-3857"],"eissn":["1469-4417"]},"day":"01","language":[{"iso":"eng"}],"publication_status":"published","corr_author":"1","external_id":{"isi":["001308182000001"]},"publication":"Ergodic Theory and Dynamical Systems","doi":"10.1017/etds.2024.48","month":"02","ddc":["510"],"issue":"2","quality_controlled":"1","date_updated":"2026-04-07T12:37:10Z","_id":"18112","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","OA_type":"hybrid","date_published":"2025-02-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)"},{"oa":1,"scopus_import":"1","oa_version":"Published Version","article_number":"14","OA_place":"publisher","year":"2025","has_accepted_license":"1","department":[{"_id":"LaEr"}],"acknowledgement":"We thank Giorgio Cipolloni for helpful discussions in a closely related joint project. Open access funding provided by Institute of Science and Technology (IST Austria). All authors were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","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)"},"file_date_updated":"2025-02-05T07:01:40Z","abstract":[{"text":"We consider two Hamiltonians that are close to each other, H1≈H2, and analyze the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2 that expresses the effect of an imperfect time reversal on the initial state ψ0. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such H1 and H2.","lang":"eng"}],"date_created":"2025-02-05T06:48:29Z","pmid":1,"article_type":"original","file":[{"content_type":"application/pdf","creator":"dernst","file_id":"19004","success":1,"date_created":"2025-02-05T07:01:40Z","access_level":"open_access","checksum":"ee07edf5f85a6f2651926b2f8760af74","file_size":828335,"date_updated":"2025-02-05T07:01:40Z","relation":"main_file","file_name":"2025_LettersMathPhysics_Erdoes.pdf"}],"title":"Loschmidt echo for deformed Wigner matrices","citation":{"mla":"Erdös, László, et al. “Loschmidt Echo for Deformed Wigner Matrices.” Letters in Mathematical Physics, vol. 115, 14, Springer Nature, 2025, doi:10.1007/s11005-025-01904-5.","ama":"Erdös L, Henheik SJ, Kolupaiev O. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 2025;115. doi:10.1007/s11005-025-01904-5","chicago":"Erdös, László, Sven Joscha Henheik, and Oleksii Kolupaiev. “Loschmidt Echo for Deformed Wigner Matrices.” Letters in Mathematical Physics. Springer Nature, 2025. https://doi.org/10.1007/s11005-025-01904-5.","ista":"Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 115, 14.","short":"L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115 (2025).","ieee":"L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner matrices,” Letters in Mathematical Physics, vol. 115. Springer Nature, 2025.","apa":"Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025). Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-01904-5"},"author":[{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"orcid":"0000-0003-1491-4623","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev"}],"doi":"10.1007/s11005-025-01904-5","month":"01","ddc":["510"],"arxiv":1,"_id":"19001","date_updated":"2026-04-07T12:37:10Z","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","date_published":"2025-01-30T00:00:00Z","OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","ec_funded":1,"intvolume":" 115","isi":1,"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"publication_identifier":{"issn":["1573-0530"]},"volume":115,"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"day":"30","language":[{"iso":"eng"}],"publication_status":"published","external_id":{"pmid":["39896265"],"isi":["001409618800002"],"arxiv":["2410.08108"]},"publication":"Letters in Mathematical Physics","corr_author":"1"},{"related_material":{"record":[{"status":"public","id":"17174","relation":"earlier_version"},{"relation":"dissertation_contains","id":"20575","status":"public"},{"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"}],"publication_identifier":{"issn":["1424-0637"]},"volume":26,"intvolume":" 26","ec_funded":1,"publisher":"Springer Nature","isi":1,"publication_status":"published","corr_author":"1","external_id":{"arxiv":["2310.06677"],"isi":["001385326500001"]},"publication":"Annales Henri Poincare","day":"01","language":[{"iso":"eng"}],"quality_controlled":"1","date_updated":"2026-04-07T12:37:11Z","_id":"18764","doi":"10.1007/s00023-024-01518-y","month":"06","arxiv":1,"ddc":["510"],"article_processing_charge":"Yes (via OA deal)","type":"journal_article","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_type":"hybrid","date_published":"2025-06-01T00:00:00Z","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":"2025-01-05T23:01:59Z","abstract":[{"text":"We prove that a class of weakly perturbed Hamiltonians of the form H_λ= H_0 + λW, with W being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by H_λ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order λ^{-2}. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix H_λ.","lang":"eng"}],"file_date_updated":"2025-06-25T05:38:34Z","page":"1991-2033","acknowledgement":"All authors were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nJ.R. was additionally supported by the ERC Advanced Grant “LDRaM” No. 884584.\r\nWe thank Peter Reimann and Lennart Dabelow for helpful comments. Open access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"LaEr"}],"title":"Prethermalization for deformed Wigner matrices","citation":{"ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner matrices,” Annales Henri Poincare, vol. 26. Springer Nature, pp. 1991–2033, 2025.","apa":"Erdös, L., Henheik, S. J., Reker, J., & Riabov, V. (2025). Prethermalization for deformed Wigner matrices. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-024-01518-y","mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” Annales Henri Poincare, vol. 26, Springer Nature, 2025, pp. 1991–2033, doi:10.1007/s00023-024-01518-y.","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025) 1991–2033.","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. 2025. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 26, 1991–2033.","ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner matrices. Annales Henri Poincare. 2025;26:1991-2033. doi:10.1007/s00023-024-01518-y","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” Annales Henri Poincare. Springer Nature, 2025. https://doi.org/10.1007/s00023-024-01518-y."},"author":[{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","full_name":"Reker, Jana","last_name":"Reker"},{"full_name":"Riabov, Volodymyr","last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"file":[{"success":1,"file_id":"19895","creator":"dernst","content_type":"application/pdf","file_name":"2025_AnnalesHenriPoincare_Erdoes.pdf","relation":"main_file","date_updated":"2025-06-25T05:38:34Z","access_level":"open_access","date_created":"2025-06-25T05:38:34Z","checksum":"49e6a934db540206f7eaa0c798553ded","file_size":977773}],"article_type":"original","scopus_import":"1","oa_version":"Published Version","oa":1,"has_accepted_license":"1","OA_place":"publisher","year":"2025"},{"year":"2025","OA_place":"repository","oa":1,"oa_version":"Preprint","citation":{"ista":"Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv, 10.48550/arXiv.2409.00677.","short":"S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.).","ama":"Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv. doi:10.48550/arXiv.2409.00677","chicago":"Henheik, Sven Joscha, Bipul Poudyal, and Roderich Tumulka. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.00677.","mla":"Henheik, Sven Joscha, et al. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, doi:10.48550/arXiv.2409.00677.","apa":"Henheik, S. J., Poudyal, B., & Tumulka, R. (n.d.). How a space-time singularity helps remove the ultraviolet divergence problem. arXiv. https://doi.org/10.48550/arXiv.2409.00677","ieee":"S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps remove the ultraviolet divergence problem,” arXiv. ."},"author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"last_name":"Poudyal","full_name":"Poudyal, Bipul","first_name":"Bipul"},{"full_name":"Tumulka, Roderich","last_name":"Tumulka","first_name":"Roderich"}],"title":"How a space-time singularity helps remove the ultraviolet divergence problem","department":[{"_id":"LaEr"}],"acknowledgement":"JH gratefully acknowledges partial financial support by the ERC Advanced\r\nGrant “RMTBeyond” No. 101020331.","abstract":[{"text":"Particle creation terms in quantum Hamiltonians are usually ultraviolet\r\ndivergent and thus mathematically ill defined. A rather novel way of solving\r\nthis problem is based on imposing so-called interior-boundary conditions on the\r\nwave function. Previous papers showed that this approach works in the\r\nnon-relativistic regime, but particle creation is mostly relevant in the\r\nrelativistic case after all. In flat relativistic space-time (that is,\r\nneglecting gravity), the approach was previously found to work only for certain\r\nsomewhat artificial cases. Here, as a way of taking gravity into account, we\r\nconsider curved space-time, specifically the super-critical\r\nReissner-Nordstr\\\"om space-time, which features a naked timelike singularity.\r\nWe find that the interior-boundary approach works fully in this setting; in\r\nparticular, we prove rigorously the existence of well-defined, self-adjoint\r\nHamiltonians with particle creation at the singularity, based on\r\ninterior-boundary conditions. We also non-rigorously analyze the asymptotic\r\nbehavior of the Bohmian trajectories and construct the corresponding Bohm-Bell\r\nprocess of particle creation, motion, and annihilation. The upshot is that in\r\nquantum physics, a naked space-time singularity need not lead to a breakdown of\r\nphysical laws, but on the contrary allows for boundary conditions governing\r\nwhat comes out of the singularity and thereby removing the ultraviolet\r\ndivergence.","lang":"eng"}],"date_created":"2025-04-11T12:07:25Z","date_published":"2025-02-28T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.00677"}],"status":"public","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"preprint","article_processing_charge":"No","arxiv":1,"doi":"10.48550/arXiv.2409.00677","month":"02","_id":"19552","date_updated":"2026-04-07T12:37:11Z","language":[{"iso":"eng"}],"day":"28","external_id":{"arxiv":["2409.00677"]},"publication":"arXiv","corr_author":"1","publication_status":"draft","ec_funded":1,"project":[{"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":"19540"}]}},{"month":"01","doi":"10.48550/arXiv.2410.10718","arxiv":1,"date_updated":"2026-04-07T12:37:11Z","_id":"19546","type":"preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10718","open_access":"1"}],"status":"public","date_published":"2025-01-30T00:00:00Z","article_processing_charge":"No","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"day":"30","language":[{"iso":"eng"}],"publication_status":"draft","corr_author":"1","publication":"arXiv","external_id":{"arxiv":["2410.10718"]},"oa":1,"oa_version":"Preprint","OA_place":"repository","year":"2025","acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"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":"2025-04-11T08:34:49Z","abstract":[{"lang":"eng","text":"We study the sensitivity of the eigenvectors of random matrices, showing that\r\neven small perturbations make the eigenvectors almost orthogonal. More\r\nprecisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show\r\nthat their bulk eigenvectors become asymptotically orthogonal as soon as\r\n$\\mathrm{Tr}(D_1-D_2)^2\\gg 1$, or their respective energies are separated on a\r\nscale much bigger than the local eigenvalue spacing. Furthermore, we show that\r\nquadratic forms of eigenvectors of $W+D_1$, $W+D_2$ with any deterministic\r\nmatrix $A\\in\\mathbf{C}^{N\\times N}$ in a specific subspace of codimension one\r\nare of size $N^{-1/2}$. This proves a generalization of the Eigenstate\r\nThermalization Hypothesis to eigenvectors belonging to two different spectral\r\nfamilies."}],"title":"Eigenvector decorrelation for random matrices","citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv. doi:10.48550/arXiv.2410.10718","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10718.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, 10.48550/arXiv.2410.10718.","mla":"Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.10718.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (n.d.). Eigenvector decorrelation for random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.10718","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” arXiv. ."},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"orcid":"0000-0003-1491-4623","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev"}]},{"month":"04","doi":"10.15479/AT-ISTA-19540","ddc":["519"],"date_updated":"2026-04-07T12:37:12Z","_id":"19540","type":"dissertation","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","status":"public","date_published":"2025-04-10T00:00:00Z","article_processing_charge":"No","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","ec_funded":1,"related_material":{"record":[{"status":"public","id":"14343","relation":"part_of_dissertation"},{"status":"public","id":"18656","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"13317","status":"public"},{"id":"11732","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"12184","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"14421","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"10623"},{"relation":"part_of_dissertation","status":"public","id":"18112"},{"relation":"part_of_dissertation","status":"public","id":"19001"},{"status":"public","id":"10642","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"19545","status":"public"},{"status":"public","id":"19546","relation":"part_of_dissertation"},{"status":"public","id":"19550","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"19551"},{"id":"19552","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"14542","relation":"part_of_dissertation"},{"id":"17049","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"18764"},{"status":"public","id":"19547","relation":"part_of_dissertation"},{"status":"public","id":"19548","relation":"part_of_dissertation"}]},"supervisor":[{"full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"isbn":["978-3-99078-057-2"],"issn":["2663-337X"]},"day":"10","language":[{"iso":"eng"}],"publication_status":"published","degree_awarded":"PhD","corr_author":"1","oa":1,"oa_version":"Published Version","OA_place":"publisher","year":"2025","has_accepted_license":"1","page":"720","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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":"2025-04-10T21:21:18Z","abstract":[{"text":"This thesis deals with several different models for complex quantum mechanical systems and is structured in three main parts. \r\n\t\r\nIn Part I, we study mean field random matrices as models for quantum Hamiltonians. Our focus lies on proving concentration estimates for resolvents of random matrices, so-called local laws, mostly in the setting of multiple resolvents. These estimates have profound consequences for eigenvector overlaps and thermalization problems. More concretely, we obtain, e.g., the optimal eigenstate thermalization hypothesis (ETH) uniformly in the spectrum for Wigner matrices, an optimal lower bound on non-Hermitian eigenvector overlaps, and prethermalization for deformed Wigner matrices.\tIn order to prove our novel multi-resolvent local laws, we develop and devise two main methods, the static Psi-method and the dynamical Zigzag strategy. \r\n\t\r\nIn Part II, we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic theory of superconductivity. We focus on asymptotic formulas for the characteristic critical temperature and energy gap of a superconductor and prove universality of their ratio in various physical regimes. Additionally, we investigate multi-band superconductors and show that inter-band coupling effects can only enhance the critical temperature. \r\n\t\r\nIn Part III, we study quantum lattice systems. On the one hand, we show a strong version of the local-perturbations-perturb-locally (LPPL) principle for the ground state of weakly interacting quantum spin systems with a uniform on-site gap. On the other hand, we introduce a notion of a local gap and rigorously justify response theory and the Kubo formula under the weakened assumption of a local gap. \r\n\t\r\nAdditionally, we discuss two classes of problems which do not fit into the three main parts of the thesis. These are deformational rigidity of Liouville metrics on the torus and relativistic toy models of particle creation via interior-boundary-conditions (IBCs). ","lang":"eng"}],"file_date_updated":"2025-04-23T14:11:05Z","file":[{"file_size":4107587,"access_level":"closed","checksum":"b8477ae5578436c72c3bb4193ad34ac5","date_created":"2025-04-10T21:14:18Z","relation":"source_file","date_updated":"2025-04-10T21:14:18Z","file_name":"Henheik-Thesis_source_final.zip","content_type":"application/zip","creator":"shenheik","file_id":"19542"},{"file_name":"Henheik-Thesis-pdfa_FINAL.pdf","date_updated":"2025-04-11T13:16:05Z","relation":"main_file","date_created":"2025-04-11T13:16:05Z","access_level":"open_access","checksum":"e9fc0ea12ec46c9f71110c33217c4140","file_size":9999492,"success":1,"creator":"shenheik","file_id":"19553","content_type":"application/pdf"},{"creator":"cchlebak","file_id":"19615","content_type":"application/pdf","file_name":"Henheik-Thesis-Volume1_print.pdf","file_size":13276442,"date_created":"2025-04-23T14:10:27Z","checksum":"f94580f86c785e7108eb116cd189e225","access_level":"closed","relation":"other","date_updated":"2025-04-23T14:10:27Z"},{"date_updated":"2025-04-23T14:11:05Z","relation":"other","file_size":7628767,"checksum":"b927ead3c78020ffb32918911deedb74","date_created":"2025-04-23T14:11:05Z","access_level":"closed","file_name":"Henheik-Thesis-Volume2_print.pdf","content_type":"application/pdf","creator":"cchlebak","file_id":"19616"}],"title":"Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems","citation":{"ieee":"S. J. Henheik, “Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems,” Institute of Science and Technology Austria, 2025.","apa":"Henheik, S. J. (2025). Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-19540","mla":"Henheik, Sven Joscha. Modeling Complex Quantum Systems : Random Matrices, BCS Theory, and Quantum Lattice Systems. Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-19540.","ista":"Henheik SJ. 2025. Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria.","short":"S.J. Henheik, Modeling Complex Quantum Systems : Random Matrices, BCS Theory, and Quantum Lattice Systems, Institute of Science and Technology Austria, 2025.","ama":"Henheik SJ. Modeling complex quantum systems : Random matrices, BCS theory, and quantum lattice systems. 2025. doi:10.15479/AT-ISTA-19540","chicago":"Henheik, Sven Joscha. “Modeling Complex Quantum Systems : Random Matrices, BCS Theory, and Quantum Lattice Systems.” Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-19540."},"author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"}]},{"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"volume":15,"publication_identifier":{"eissn":["1664-0403"]},"publisher":"EMS Press","intvolume":" 15","ec_funded":1,"isi":1,"publication_status":"published","corr_author":"1","publication":"Journal of Spectral Theory","external_id":{"arxiv":["2312.11310"],"isi":["001438931600009"]},"day":"09","language":[{"iso":"eng"}],"quality_controlled":"1","date_updated":"2026-04-07T12:37:11Z","_id":"19548","month":"01","doi":"10.4171/JST/540","arxiv":1,"ddc":["500"],"issue":"1","article_processing_charge":"No","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"gold","date_published":"2025-01-09T00:00:00Z","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":"2025-04-11T09:19:28Z","file_date_updated":"2025-04-11T09:13:31Z","abstract":[{"lang":"eng","text":"We consider the BCS energy gap „.T / (essentially given by „.T / \u0019 .T; p\u0016/,\r\nthe BCS order parameter) at all temperatures 0 \u0014 T \u0014 Tc up to the critical one, Tc, and show\r\nthat, in the limit of weak coupling, the ratio „.T /=Tc is given by a universal function of the relative temperature T =Tc. On the one hand, this recovers a recent result by Langmann and Triola\r\n[Phys. Rev. B 108 (2023), no. 10, article no. 104503] on three-dimensional s-wave superconductors for temperatures bounded uniformly away from Tc. On the other hand, our result lifts these\r\nrestrictions, as we consider arbitrary spatial dimensions d 2 ¹1; 2; 3º, discuss superconductors\r\nwith non-zero angular momentum (primarily in two dimensions), and treat the perhaps physically most interesting (due to the occurrence of the superconducting phase transition) regime of\r\ntemperatures close to Tc.\r\n\r\n\r\n ."}],"page":"305–352","acknowledgement":"We thank Andreas Deuchert, Christian Hainzl, Edwin Langmann, Marius Lemm, Robert Seiringer, and Jan Philip Solovej for helpful discussions,\r\nand Edwin Langmann and Robert Seiringer for valuable comments on an earlier version of the manuscript.\r\nFunding. Joscha Henheik gratefully acknowledges partial financial support by the\r\nERC Advanced Grant “RMTBeyond” No. 101020331. Asbjørn Bækgaard Lauritsen\r\ngratefully acknowledges partial financial support by the Austrian Science Fund (FWF)\r\nthrough grant DOI 10.55776/I6427 (as part of the SFB/TRR 352).\r\n","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"title":"Universal behavior of the BCS energy gap","DOAJ_listed":"1","author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288"}],"citation":{"mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” Journal of Spectral Theory, vol. 15, no. 1, EMS Press, 2025, pp. 305–352, doi:10.4171/JST/540.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” Journal of Spectral Theory. EMS Press, 2025. https://doi.org/10.4171/JST/540.","ama":"Henheik SJ, Lauritsen AB. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 2025;15(1):305–352. doi:10.4171/JST/540","short":"S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.","ista":"Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352.","ieee":"S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,” Journal of Spectral Theory, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.","apa":"Henheik, S. J., & Lauritsen, A. B. (2025). Universal behavior of the BCS energy gap. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/540"},"file":[{"success":1,"file_id":"19549","creator":"cchlebak","content_type":"application/pdf","file_name":"Henheik_JSpectralTheory_2025.pdf","relation":"main_file","date_updated":"2025-04-11T09:13:31Z","checksum":"f49e06e8dba819f7ad52a202e287ebca","date_created":"2025-04-11T09:13:31Z","access_level":"open_access","file_size":779158}],"article_type":"original","scopus_import":"1","oa_version":"Published Version","oa":1,"has_accepted_license":"1","OA_place":"publisher","year":"2025"},{"year":"2024","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","file":[{"content_type":"application/pdf","file_id":"17300","creator":"dernst","success":1,"file_size":555070,"access_level":"open_access","checksum":"f7793d313104c70422140c5e6494c779","date_created":"2024-07-22T09:41:21Z","relation":"main_file","date_updated":"2024-07-22T09:41:21Z","file_name":"2024_JourTheorProbab_Campbell.pdf"}],"article_type":"original","author":[{"full_name":"Campbell, Andrew J","last_name":"Campbell","first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"first_name":"Sean","last_name":"O’Rourke","full_name":"O’Rourke, Sean"}],"citation":{"apa":"Campbell, A. J., & O’Rourke, S. (2024). Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. Springer Nature. https://doi.org/10.1007/s10959-023-01275-4","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” Journal of Theoretical Probability, vol. 37. Springer Nature, pp. 933–973, 2024.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability. Springer Nature, 2024. https://doi.org/10.1007/s10959-023-01275-4.","ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 2024;37:933-973. doi:10.1007/s10959-023-01275-4","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973.","ista":"Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 37, 933–973.","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability, vol. 37, Springer Nature, 2024, pp. 933–73, doi:10.1007/s10959-023-01275-4."},"title":"Spectrum of Lévy–Khintchine random laplacian matrices","acknowledgement":"The first author thanks Yizhe Zhu for pointing out reference [30]. We thank David Renfrew for comments on an earlier draft. We thank the anonymous referee for a careful reading and helpful comments.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"LaEr"}],"page":"933-973","date_created":"2023-08-06T22:01:13Z","abstract":[{"text":"We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure.","lang":"eng"}],"file_date_updated":"2024-07-22T09:41:21Z","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":"2024-03-01T00:00:00Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","article_processing_charge":"Yes (via OA deal)","arxiv":1,"ddc":["510"],"doi":"10.1007/s10959-023-01275-4","month":"03","quality_controlled":"1","date_updated":"2024-07-22T09:41:42Z","_id":"13975","language":[{"iso":"eng"}],"day":"01","corr_author":"1","publication":"Journal of Theoretical Probability","external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"publication_status":"published","isi":1,"intvolume":" 37","publisher":"Springer Nature","volume":37,"publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]}},{"article_type":"original","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01229-1.","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 2024;188:1131-1182. doi:10.1007/s00440-023-01229-1","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2024. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 188, 1131–1182.","mla":"Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:10.1007/s00440-023-01229-1.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” Probability Theory and Related Fields, vol. 188. Springer Nature, pp. 1131–1182, 2024."},"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","department":[{"_id":"LaEr"}],"acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.\r\nLászló Erdős supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Dominik Schröder supported by the SNSF Ambizione Grant PZ00P2 209089.","page":"1131-1182","abstract":[{"lang":"eng","text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0Electronic Journal of Probability, vol. 29. Institute of Mathematical Statistics, 2024.","apa":"Reker, J. (2024). Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-EJP1247","mla":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” Electronic Journal of Probability, vol. 29, 191, Institute of Mathematical Statistics, 2024, doi:10.1214/24-EJP1247.","chicago":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/24-EJP1247.","ama":"Reker J. Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. 2024;29. doi:10.1214/24-EJP1247","short":"J. Reker, Electronic Journal of Probability 29 (2024).","ista":"Reker J. 2024. Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. 29, 191."},"author":[{"full_name":"Reker, Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana"}],"oa":1,"scopus_import":"1","oa_version":"Published Version","OA_place":"publisher","article_number":"191","year":"2024","has_accepted_license":"1"},{"year":"2024","oa":1,"oa_version":"Preprint","scopus_import":"1","article_type":"original","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"orcid":"0000-0003-2625-495X","id":"b0cc634c-d549-11ee-96c8-87338c7ad808","first_name":"Benjamin","full_name":"McKenna, Benjamin","last_name":"McKenna"}],"citation":{"mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000.","ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 2024;34(1B):1623-1662. doi:10.1214/23-AAP2000","chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000.","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","apa":"Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-AAP2000"},"title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","department":[{"_id":"LaEr"}],"acknowledgement":"The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation.","page":"1623-1662","abstract":[{"lang":"eng","text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble."}],"date_created":"2024-02-25T23:00:56Z","date_published":"2024-02-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2208.12206","open_access":"1"}],"type":"journal_article","article_processing_charge":"No","issue":"1B","arxiv":1,"month":"02","doi":"10.1214/23-AAP2000","_id":"15025","quality_controlled":"1","date_updated":"2025-09-04T12:08:11Z","language":[{"iso":"eng"}],"day":"01","publication":"Annals of Applied Probability","external_id":{"arxiv":["2208.12206"],"isi":["001163006100021"]},"corr_author":"1","publication_status":"published","isi":1,"ec_funded":1,"intvolume":" 34","publisher":"Institute of Mathematical Statistics","volume":34,"publication_identifier":{"issn":["1050-5164"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}]},{"scopus_import":"1","oa_version":"Published Version","oa":1,"has_accepted_license":"1","OA_place":"publisher","year":"2024","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)"},"file_date_updated":"2025-01-09T09:36:41Z","abstract":[{"lang":"eng","text":"We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest."}],"date_created":"2024-05-12T22:01:02Z","page":"3785-3840","department":[{"_id":"LaEr"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","acknowledgement":"László Erdős is partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Hong Chang Ji is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","citation":{"ama":"Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 2024;77(9):3785-3840. doi:10.1002/cpa.22201","chicago":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics. Wiley, 2024. https://doi.org/10.1002/cpa.22201.","short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840.","ista":"Erdös L, Ji HC. 2024. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 77(9), 3785–3840.","mla":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:10.1002/cpa.22201.","apa":"Erdös, L., & Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22201","ieee":"L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” Communications on Pure and Applied Mathematics, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024."},"author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","last_name":"Ji","full_name":"Ji, Hong Chang"}],"article_type":"original","file":[{"content_type":"application/pdf","success":1,"creator":"dernst","file_id":"18803","date_updated":"2025-01-09T09:36:41Z","relation":"main_file","file_size":566963,"access_level":"open_access","date_created":"2025-01-09T09:36:41Z","checksum":"fbcc9cc7bf274f024e4f4afc9c208f96","file_name":"2024_CommPureApplMath_Erdoes.pdf"}],"_id":"15378","quality_controlled":"1","date_updated":"2025-09-08T07:25:47Z","doi":"10.1002/cpa.22201","month":"09","ddc":["510"],"issue":"9","arxiv":1,"article_processing_charge":"Yes (via OA deal)","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","date_published":"2024-09-01T00:00:00Z","OA_type":"hybrid","volume":77,"publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"Wiley","intvolume":" 77","ec_funded":1,"isi":1,"publication_status":"published","external_id":{"isi":["001217139900001"],"arxiv":["2301.04981"]},"publication":"Communications on Pure and Applied Mathematics","corr_author":"1","day":"01","language":[{"iso":"eng"}]},{"date_published":"2024-07-01T00:00:00Z","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"issue":"13","month":"07","doi":"10.1093/imrn/rnae062","date_updated":"2025-09-08T08:16:32Z","quality_controlled":"1","_id":"17281","language":[{"iso":"eng"}],"day":"01","corr_author":"1","external_id":{"isi":["001198019500001"]},"publication":"International Mathematics Research Notices","publication_status":"published","isi":1,"intvolume":" 2024","publisher":"Oxford University Press","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"volume":2024,"year":"2024","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","file":[{"success":1,"file_id":"17288","creator":"dernst","content_type":"application/pdf","file_name":"2024_IMRN_Campbell.pdf","date_updated":"2024-07-22T06:40:19Z","relation":"main_file","access_level":"open_access","checksum":"f36a7dbf53f23d5833db711052e69b49","date_created":"2024-07-22T06:40:19Z","file_size":1233508}],"article_type":"original","author":[{"last_name":"Campbell","full_name":"Campbell, Andrew J","first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"first_name":"Sean","last_name":"O'Rourke","full_name":"O'Rourke, Sean"},{"full_name":"Renfrew, David T","last_name":"Renfrew","orcid":"0000-0003-3493-121X","first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87"}],"citation":{"apa":"Campbell, A. J., O’Rourke, S., & Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae062","ieee":"A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation,” International Mathematics Research Notices, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024.","ama":"Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024;2024(13):10189-10218. doi:10.1093/imrn/rnae062","chicago":"Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae062.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218.","ista":"Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024(13), 10189–10218.","mla":"Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” International Mathematics Research Notices, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:10.1093/imrn/rnae062."},"title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","acknowledgement":"This work was supported by the National Science Foundation [Grant No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The third author acknowledges the support of the University of Colorado Boulder, where a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin, Brian Hall, and Noah Williams for comments, corrections, and references. The authors also wish to thank the anonymous referees for useful feedback and corrections.","department":[{"_id":"LaEr"}],"page":"10189-10218","date_created":"2024-07-21T22:01:01Z","file_date_updated":"2024-07-22T06:40:19Z","abstract":[{"lang":"eng","text":"We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions."}],"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)"}},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"issn":["0022-2488"]},"volume":65,"intvolume":" 65","ec_funded":1,"publisher":"AIP Publishing","isi":1,"publication_status":"published","corr_author":"1","external_id":{"isi":["001252240700002"],"arxiv":["2210.15643"]},"publication":"Journal of Mathematical Physics","day":"01","language":[{"iso":"eng"}],"date_updated":"2025-09-08T08:44:57Z","quality_controlled":"1","_id":"17375","month":"06","doi":"10.1063/5.0209705","arxiv":1,"issue":"6","article_processing_charge":"No","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.15643"}],"date_published":"2024-06-01T00:00:00Z","date_created":"2024-08-04T22:01:22Z","abstract":[{"lang":"eng","text":"We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion."}],"acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","department":[{"_id":"LaEr"}],"title":"Precise asymptotics for the spectral radius of a large random matrix","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","orcid":"0000-0003-1559-1205","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"citation":{"ama":"Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 2024;65(6). doi:10.1063/5.0209705","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” Journal of Mathematical Physics. AIP Publishing, 2024. https://doi.org/10.1063/5.0209705.","ista":"Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","mla":"Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” Journal of Mathematical Physics, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:10.1063/5.0209705.","apa":"Cipolloni, G., Erdös, L., & Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0209705","ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” Journal of Mathematical Physics, vol. 65, no. 6. AIP Publishing, 2024."},"article_type":"original","scopus_import":"1","oa_version":"Preprint","oa":1,"article_number":"063302","year":"2024"},{"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"LaEr"}],"date_created":"2024-11-17T23:01:46Z","file_date_updated":"2024-11-18T08:15:07Z","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure."}],"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)"},"file":[{"file_name":"2024_CommMathPhysics_Erdoes.pdf","date_updated":"2024-11-18T08:15:07Z","relation":"main_file","file_size":1426046,"date_created":"2024-11-18T08:15:07Z","checksum":"c9ae0ea195bd39b8b3a630d492fb00dc","access_level":"open_access","success":1,"creator":"dernst","file_id":"18562","content_type":"application/pdf"}],"article_type":"original","pmid":1,"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Riabov","full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"}],"citation":{"apa":"Erdös, L., & Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-024-05143-y","ieee":"L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” Communications in Mathematical Physics, vol. 405, no. 12. Springer Nature, 2024.","ama":"Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 2024;405(12). doi:10.1007/s00220-024-05143-y","chicago":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” Communications in Mathematical Physics. Springer Nature, 2024. https://doi.org/10.1007/s00220-024-05143-y.","short":"L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).","ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282.","mla":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” Communications in Mathematical Physics, vol. 405, no. 12, 282, Springer Nature, 2024, doi:10.1007/s00220-024-05143-y."},"title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices","oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2024","OA_place":"publisher","article_number":"282","has_accepted_license":"1","isi":1,"publisher":"Springer Nature","intvolume":" 405","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"volume":405,"related_material":{"record":[{"relation":"dissertation_contains","id":"20575","status":"public"}]},"language":[{"iso":"eng"}],"day":"01","corr_author":"1","publication":"Communications in Mathematical Physics","external_id":{"isi":["001348943900004"],"arxiv":["2403.10359"],"pmid":["39526190"]},"publication_status":"published","arxiv":1,"ddc":["510"],"issue":"12","doi":"10.1007/s00220-024-05143-y","month":"12","quality_controlled":"1","date_updated":"2026-04-07T12:32:19Z","_id":"18554","OA_type":"hybrid","date_published":"2024-12-01T00:00:00Z","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","article_processing_charge":"Yes (via OA deal)"},{"language":[{"iso":"eng"}],"day":"30","publication":"Advances in Theoretical and Mathematical Physics","external_id":{"arxiv":["2402.17609"]},"corr_author":"1","publication_status":"published","publisher":"International Press","intvolume":" 28","ec_funded":1,"volume":28,"publication_identifier":{"eissn":["1095-0753"],"issn":["1095-0761"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"date_published":"2024-10-30T00:00:00Z","OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2402.17609","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_processing_charge":"No","issue":"6","arxiv":1,"doi":"10.4310/ATMP.241031013250","month":"10","_id":"18656","quality_controlled":"1","date_updated":"2026-04-07T12:37:10Z","article_type":"original","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","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik"}],"citation":{"ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6. International Press, pp. 2025–2083, 2024.","apa":"Cipolloni, G., Erdös, L., & Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.241031013250","mla":"Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics, vol. 28, no. 6, International Press, 2024, pp. 2025–83, doi:10.4310/ATMP.241031013250.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2024. https://doi.org/10.4310/ATMP.241031013250.","ama":"Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 2024;28(6):2025-2083. doi:10.4310/ATMP.241031013250","ista":"Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083."},"title":"Out-of-time-ordered correlators for Wigner matrices","department":[{"_id":"LaEr"}],"acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","page":"2025-2083","abstract":[{"text":"We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables \r\n and \r\n in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11]).","lang":"eng"}],"date_created":"2024-12-15T23:01:51Z","year":"2024","OA_place":"repository","oa":1,"oa_version":"Preprint","scopus_import":"1"}]