[{"date_created":"2025-10-16T13:10:26Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"article_type":"original","ec_funded":1,"_id":"20478","month":"09","oa_version":"Published Version","publication":"Probability Theory and Related Fields","isi":1,"date_updated":"2026-06-18T18:23:40Z","oa":1,"citation":{"ama":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s00440-025-01422-4\">10.1007/s00440-025-01422-4</a>","mla":"Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00440-025-01422-4\">10.1007/s00440-025-01422-4</a>.","ista":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields.","short":"Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025).","ieee":"Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation transition in the Wigner minor process,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025.","chicago":"Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01422-4\">https://doi.org/10.1007/s00440-025-01422-4</a>.","apa":"Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025). Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01422-4\">https://doi.org/10.1007/s00440-025-01422-4</a>"},"OA_place":"publisher","publication_status":"epub_ahead","year":"2025","doi":"10.1007/s00440-025-01422-4","OA_type":"hybrid","quality_controlled":"1","status":"public","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"publisher":"Springer Nature","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121 and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","title":"Decorrelation transition in the Wigner minor process","abstract":[{"text":"We consider the Wigner minor process, i.e. the eigenvalues of an N\\times N Wigner matrix H^{(N)} together with the eigenvalues of all its n\\times n minors, H^{(n)}, n\\le N. The top eigenvalues of H^{(N)} and those of its immediate minor H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical transition regime around k\\sim N^{2/3} was analyzed by Forrester and Nagao (J. Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality.","lang":"eng"}],"ddc":["500"],"fulldoi":"https://doi.org/10.1007/s00440-025-01422-4","external_id":{"arxiv":["2503.06549"],"isi":["001574640900001"]},"date_published":"2025-09-20T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"corr_author":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-025-01422-4"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"scopus_import":"1","author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475"},{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Kolupaiev","orcid":"0000-0003-1491-4623","full_name":"Kolupaiev, Oleksii","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"day":"20","type":"journal_article","PlanS_conform":"1","article_processing_charge":"Yes (via OA deal)"},{"ec_funded":1,"_id":"20576","month":"06","fulldoi":"https://doi.org/10.48550/ARXIV.2506.06441","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2025-10-29T19:09:03Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"20575"}]},"date_updated":"2026-04-07T12:32:19Z","language":[{"iso":"eng"}],"oa":1,"oa_version":"Preprint","publication":"arXiv","date_published":"2025-06-06T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2506.06441"}],"doi":"10.48550/ARXIV.2506.06441","author":[{"full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"full_name":"Riabov, Volodymyr","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov"}],"corr_author":"1","publication_status":"draft","OA_place":"repository","citation":{"ama":"Erdös L, Riabov V. The zigzag strategy for random band matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">10.48550/ARXIV.2506.06441</a>","mla":"Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">10.48550/ARXIV.2506.06441</a>.","ista":"Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">10.48550/ARXIV.2506.06441</a>.","short":"L. Erdös, V. Riabov, ArXiv (n.d.).","ieee":"L. Erdös and V. Riabov, “The zigzag strategy for random band matrices,” <i>arXiv</i>. .","chicago":"Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">https://doi.org/10.48550/ARXIV.2506.06441</a>.","apa":"Erdös, L., &#38; Riabov, V. (n.d.). The zigzag strategy for random band matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2506.06441\">https://doi.org/10.48550/ARXIV.2506.06441</a>"},"year":"2025","type":"preprint","acknowledgement":" Supported by the ERC\r\nAdvanced Grant ”RMTBeyond” No. 101020331.","abstract":[{"lang":"eng","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."}],"title":"The zigzag strategy for random band matrices","article_processing_charge":"No","status":"public","day":"06","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}]},{"status":"public","abstract":[{"lang":"eng","text":"We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof are a noncancellation result for the wave trace and an analysis of the second order variational formula for the energy functional associated to closed geodesics. Noncancellation allows us to detect parts of the length spectrum from the Laplace spectrum and conclude rational integrability for the deformed geodesic flow (Liouville metrics are folklorically conjectured to be the only Riemannian metrics with integrable geodesic flow on the torus). We then use the second variational formula to show how the preservation of a single rational torus is sufficient to conclude triviality of the deformation, assuming linearity. We also present some evidence that our hypothesis of linearity may indeed be necessary."}],"title":"Spectral rigidity of Liouville tori","publication_status":"draft","citation":{"ista":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">10.48550/ARXIV.2511.10398</a>.","ama":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">10.48550/ARXIV.2511.10398</a>","mla":"Henheik, Sven Joscha, et al. “Spectral Rigidity of Liouville Tori.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">10.48550/ARXIV.2511.10398</a>.","chicago":"Henheik, Sven Joscha, Vadim Kaloshin, Yunzhe Li, and Amir Vig. “Spectral Rigidity of Liouville Tori.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">https://doi.org/10.48550/ARXIV.2511.10398</a>.","apa":"Henheik, S. J., Kaloshin, V., Li, Y., &#38; Vig, A. (n.d.). Spectral rigidity of Liouville tori. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">https://doi.org/10.48550/ARXIV.2511.10398</a>","short":"S.J. Henheik, V. Kaloshin, Y. Li, A. Vig, ArXiv (n.d.).","ieee":"S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville tori,” <i>arXiv</i>. ."},"OA_place":"repository","year":"2025","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"doi":"10.48550/ARXIV.2511.10398","OA_type":"green","publication":"arXiv","oa_version":"Preprint","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"22255"}]},"date_updated":"2026-07-20T14:58:23Z","oa":1,"date_created":"2026-07-14T12:51:50Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"VaKa"},{"_id":"LaEr"}],"_id":"22340","month":"11","day":"13","type":"preprint","article_processing_charge":"No","corr_author":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2511.10398","open_access":"1"}],"author":[{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Li","id":"41cb05d3-f128-11eb-9611-e4e2b3cfba31","first_name":"Yunzhe","full_name":"Li, Yunzhe"},{"full_name":"Vig, Amir","first_name":"Amir","id":"49d58dd5-45f5-11ec-9f86-8ce1276989b9","last_name":"Vig"}],"external_id":{"arxiv":["2511.10398"]},"date_published":"2025-11-13T00:00:00Z","arxiv":1,"keyword":["Differential Geometry (math.DG)","Mathematical Physics (math-ph)","Dynamical Systems (math.DS)","Spectral Theory (math.SP)","FOS: Mathematics","FOS: Mathematics","FOS: Physical sciences","FOS: Physical sciences","58J42","37J35","37J35","35P20","58J40","58J50","37D40"],"language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.48550/ARXIV.2511.10398"},{"quality_controlled":"1","publisher":"Cambridge University Press","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020"}],"issue":"2","status":"public","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.","title":"Deformational rigidity of integrable metrics on the torus","abstract":[{"lang":"eng","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."}],"OA_place":"publisher","publication_status":"published","citation":{"mla":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 45, no. 2, Cambridge University Press, 2025, pp. 467–503, doi:<a href=\"https://doi.org/10.1017/etds.2024.48\">10.1017/etds.2024.48</a>.","ama":"Henheik SJ. Deformational rigidity of integrable metrics on the torus. <i>Ergodic Theory and Dynamical Systems</i>. 2025;45(2):467-503. doi:<a href=\"https://doi.org/10.1017/etds.2024.48\">10.1017/etds.2024.48</a>","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,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 45, no. 2. Cambridge University Press, pp. 467–503, 2025.","short":"S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503.","apa":"Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the torus. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2024.48\">https://doi.org/10.1017/etds.2024.48</a>","chicago":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/etds.2024.48\">https://doi.org/10.1017/etds.2024.48</a>."},"year":"2025","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"volume":45,"doi":"10.1017/etds.2024.48","OA_type":"hybrid","oa_version":"Published Version","publication":"Ergodic Theory and Dynamical Systems","intvolume":"        45","file_date_updated":"2025-01-13T08:51:40Z","related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"oa":1,"isi":1,"file":[{"success":1,"file_id":"18828","date_updated":"2025-01-13T08:51:40Z","file_name":"2025_ErgodicTheory_Henheik.pdf","creator":"dernst","file_size":659100,"checksum":"650fe115d998fe0ac3a8d0c7519447c8","relation":"main_file","access_level":"open_access","date_created":"2025-01-13T08:51:40Z","content_type":"application/pdf"}],"date_updated":"2026-07-29T13:18:16Z","date_created":"2024-09-22T22:01:43Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","department":[{"_id":"LaEr"}],"ec_funded":1,"_id":"18112","month":"02","day":"01","type":"journal_article","article_processing_charge":"Yes (via OA deal)","page":"467-503","corr_author":"1","scopus_import":"1","publication_identifier":{"eissn":["1469-4417"],"issn":["0143-3857"]},"author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"}],"date_published":"2025-02-01T00:00:00Z","external_id":{"isi":["001308182000001"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","fulldoi":"https://doi.org/10.1017/etds.2024.48","ddc":["510"]},{"publication_status":"published","citation":{"mla":"Erdös, László, et al. “Loschmidt Echo for Deformed Wigner Matrices.” <i>Letters in Mathematical Physics</i>, vol. 115, 14, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s11005-025-01904-5\">10.1007/s11005-025-01904-5</a>.","ama":"Erdös L, Henheik SJ, Kolupaiev O. Loschmidt echo for deformed Wigner matrices. <i>Letters in Mathematical Physics</i>. 2025;115. doi:<a href=\"https://doi.org/10.1007/s11005-025-01904-5\">10.1007/s11005-025-01904-5</a>","ista":"Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner matrices. Letters in Mathematical Physics. 115, 14.","ieee":"L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner matrices,” <i>Letters in Mathematical Physics</i>, vol. 115. Springer Nature, 2025.","short":"L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115 (2025).","apa":"Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025). Loschmidt echo for deformed Wigner matrices. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-025-01904-5\">https://doi.org/10.1007/s11005-025-01904-5</a>","chicago":"Erdös, László, Sven Joscha Henheik, and Oleksii Kolupaiev. “Loschmidt Echo for Deformed Wigner Matrices.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11005-025-01904-5\">https://doi.org/10.1007/s11005-025-01904-5</a>."},"OA_place":"publisher","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2025","volume":115,"doi":"10.1007/s11005-025-01904-5","OA_type":"hybrid","quality_controlled":"1","status":"public","publisher":"Springer Nature","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"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.","title":"Loschmidt echo for deformed Wigner matrices","abstract":[{"lang":"eng","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-02-05T06:48:29Z","department":[{"_id":"LaEr"}],"article_type":"original","_id":"19001","ec_funded":1,"month":"01","oa_version":"Published Version","publication":"Letters in Mathematical Physics","file_date_updated":"2025-02-05T07:01:40Z","intvolume":"       115","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"isi":1,"file":[{"file_name":"2025_LettersMathPhysics_Erdoes.pdf","creator":"dernst","file_id":"19004","date_updated":"2025-02-05T07:01:40Z","success":1,"content_type":"application/pdf","date_created":"2025-02-05T07:01:40Z","access_level":"open_access","relation":"main_file","checksum":"ee07edf5f85a6f2651926b2f8760af74","file_size":828335}],"date_updated":"2026-07-29T13:18:16Z","oa":1,"corr_author":"1","article_number":"14","scopus_import":"1","publication_identifier":{"issn":["1573-0530"]},"author":[{"full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"full_name":"Kolupaiev, Oleksii","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev"}],"day":"30","type":"journal_article","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","ddc":["510"],"fulldoi":"https://doi.org/10.1007/s11005-025-01904-5","date_published":"2025-01-30T00:00:00Z","external_id":{"isi":["001409618800002"],"pmid":["39896265"],"arxiv":["2410.08108"]},"pmid":1,"arxiv":1,"language":[{"iso":"eng"}]},{"oa":1,"isi":1,"date_updated":"2026-07-29T13:18:17Z","file":[{"file_name":"Henheik_JSpectralTheory_2025.pdf","creator":"cchlebak","success":1,"date_updated":"2025-04-11T09:13:31Z","file_id":"19549","access_level":"open_access","date_created":"2025-04-11T09:13:31Z","content_type":"application/pdf","file_size":779158,"checksum":"f49e06e8dba819f7ad52a202e287ebca","relation":"main_file"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"intvolume":"        15","file_date_updated":"2025-04-11T09:13:31Z","publication":"Journal of Spectral Theory","oa_version":"Published Version","month":"01","DOAJ_listed":"1","ec_funded":1,"_id":"19548","article_type":"original","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-04-11T09:19:28Z","title":"Universal behavior of the BCS energy gap","abstract":[{"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 .","lang":"eng"}],"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","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"publisher":"EMS Press","status":"public","issue":"1","quality_controlled":"1","OA_type":"gold","doi":"10.4171/JST/540","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2025","volume":15,"publication_status":"published","OA_place":"publisher","citation":{"mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>, vol. 15, no. 1, EMS Press, 2025, pp. 305–352, doi:<a href=\"https://doi.org/10.4171/JST/540\">10.4171/JST/540</a>.","ama":"Henheik SJ, Lauritsen AB. Universal behavior of the BCS energy gap. <i>Journal of Spectral Theory</i>. 2025;15(1):305–352. doi:<a href=\"https://doi.org/10.4171/JST/540\">10.4171/JST/540</a>","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,” <i>Journal of Spectral Theory</i>, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2025). Universal behavior of the BCS energy gap. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/540\">https://doi.org/10.4171/JST/540</a>","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/JST/540\">https://doi.org/10.4171/JST/540</a>."},"language":[{"iso":"eng"}],"arxiv":1,"external_id":{"isi":["001438931600009"],"arxiv":["2312.11310"]},"date_published":"2025-01-09T00:00:00Z","fulldoi":"https://doi.org/10.4171/JST/540","ddc":["500"],"has_accepted_license":"1","article_processing_charge":"No","type":"journal_article","day":"09","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Lauritsen","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard"}],"scopus_import":"1","publication_identifier":{"eissn":["1664-0403"]},"corr_author":"1","page":"305–352"},{"department":[{"_id":"LaEr"}],"date_created":"2025-04-11T12:07:25Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"02","ec_funded":1,"_id":"19552","oa_version":"Preprint","publication":"arXiv","date_updated":"2026-07-29T13:18:16Z","oa":1,"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"year":"2025","publication_status":"draft","OA_place":"repository","citation":{"apa":"Henheik, S. J., Poudyal, B., &#38; Tumulka, R. (n.d.). How a space-time singularity helps remove the ultraviolet divergence problem. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2409.00677\">https://doi.org/10.48550/arXiv.2409.00677</a>","chicago":"Henheik, Sven Joscha, Bipul Poudyal, and Roderich Tumulka. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2409.00677\">https://doi.org/10.48550/arXiv.2409.00677</a>.","ieee":"S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps remove the ultraviolet divergence problem,” <i>arXiv</i>. .","short":"S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.).","ista":"Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2409.00677\">10.48550/arXiv.2409.00677</a>.","mla":"Henheik, Sven Joscha, et al. “How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2409.00677\">10.48550/arXiv.2409.00677</a>.","ama":"Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove the ultraviolet divergence problem. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2409.00677\">10.48550/arXiv.2409.00677</a>"},"doi":"10.48550/arXiv.2409.00677","status":"public","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"title":"How a space-time singularity helps remove the ultraviolet divergence problem","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"}],"acknowledgement":"JH gratefully acknowledges partial financial support by the ERC Advanced\r\nGrant “RMTBeyond” No. 101020331.","fulldoi":"https://doi.org/10.48550/arXiv.2409.00677","arxiv":1,"external_id":{"arxiv":["2409.00677"]},"date_published":"2025-02-28T00:00:00Z","language":[{"iso":"eng"}],"corr_author":"1","author":[{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"last_name":"Poudyal","full_name":"Poudyal, Bipul","first_name":"Bipul"},{"last_name":"Tumulka","full_name":"Tumulka, Roderich","first_name":"Roderich"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.00677","open_access":"1"}],"day":"28","article_processing_charge":"No","type":"preprint"},{"corr_author":"1","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"last_name":"Kolupaiev","orcid":"0000-0003-1491-4623","full_name":"Kolupaiev, Oleksii","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.10718"}],"day":"30","article_processing_charge":"No","type":"preprint","fulldoi":"https://doi.org/10.48550/arXiv.2410.10718","arxiv":1,"date_published":"2025-01-30T00:00:00Z","external_id":{"arxiv":["2410.10718"]},"language":[{"iso":"eng"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2025","OA_place":"repository","publication_status":"draft","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>arXiv</i>. .","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.10718\">https://doi.org/10.48550/arXiv.2410.10718</a>.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (n.d.). Eigenvector decorrelation for random matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.10718\">https://doi.org/10.48550/arXiv.2410.10718</a>","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10718\">10.48550/arXiv.2410.10718</a>","mla":"Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10718\">10.48550/arXiv.2410.10718</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.10718\">10.48550/arXiv.2410.10718</a>."},"doi":"10.48550/arXiv.2410.10718","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"status":"public","abstract":[{"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.","lang":"eng"}],"title":"Eigenvector decorrelation for random matrices","acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2025-04-11T08:34:49Z","month":"01","_id":"19546","ec_funded":1,"publication":"arXiv","oa_version":"Preprint","oa":1,"date_updated":"2026-09-16T10:00:54Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"},{"id":"22923","status":"public","relation":"later_version"}]}},{"ec_funded":1,"_id":"20575","month":"11","date_created":"2025-10-29T19:12:24Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"related_material":{"record":[{"id":"20322","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"13317","status":"public"},{"status":"deleted","id":"19368","relation":"part_of_dissertation"},{"status":"public","id":"20576","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"17174"},{"relation":"part_of_dissertation","id":"19547","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"19598"},{"relation":"part_of_dissertation","id":"18554","status":"public"},{"status":"public","id":"18764","relation":"part_of_dissertation"}]},"date_updated":"2026-10-16T08:41:47Z","file":[{"date_created":"2025-10-29T18:53:59Z","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_size":7536583,"checksum":"6a0487b2b66bb35d44b394756d44b8b4","creator":"vriabov","file_name":"riabov_thesis-pdfa.pdf","success":1,"date_updated":"2025-10-29T18:53:59Z","file_id":"20577"},{"file_name":"manuscript.zip","creator":"vriabov","file_id":"20578","date_updated":"2025-10-29T18:54:53Z","access_level":"closed","content_type":"application/x-zip-compressed","date_created":"2025-10-29T18:54:53Z","file_size":17841612,"checksum":"224efda6bf9864d296a1e5e0124c1e8f","relation":"source_file"}],"oa":1,"oa_version":"Published Version","file_date_updated":"2025-10-29T18:54:53Z","doi":"10.15479/AT-ISTA-20575","OA_place":"publisher","citation":{"apa":"Riabov, V. (2025). <i>Universality in random matrices with spatial structure</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-20575\">https://doi.org/10.15479/AT-ISTA-20575</a>","chicago":"Riabov, Volodymyr. “Universality in Random Matrices with Spatial Structure.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-20575\">https://doi.org/10.15479/AT-ISTA-20575</a>.","ieee":"V. Riabov, “Universality in random matrices with spatial structure,” Institute of Science and Technology Austria, 2025.","short":"V. Riabov, Universality in Random Matrices with Spatial Structure, Institute of Science and Technology Austria, 2025.","ista":"Riabov V. 2025. Universality in random matrices with spatial structure. Institute of Science and Technology Austria.","mla":"Riabov, Volodymyr. <i>Universality in Random Matrices with Spatial Structure</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20575\">10.15479/AT-ISTA-20575</a>.","ama":"Riabov V. Universality in random matrices with spatial structure. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20575\">10.15479/AT-ISTA-20575</a>"},"publication_status":"published","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2025","acknowledgement":"The work comprising this thesis was supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo.101020331 awarded to my advisor.","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"}],"title":"Universality in random matrices with spatial structure","supervisor":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László"}],"status":"public","publisher":"Institute of Science and Technology Austria","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"has_accepted_license":"1","ddc":["515","519"],"degree_awarded":"PhD","fulldoi":"https://doi.org/10.15479/AT-ISTA-20575","language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"date_published":"2025-11-03T00:00:00Z","publication_identifier":{"isbn":["978-3-99078-064-0"],"issn":["2663-337X"]},"author":[{"last_name":"Riabov","full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr"}],"corr_author":"1","page":"436","type":"dissertation","article_processing_charge":"No","day":"3"},{"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"}],"title":"Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems","supervisor":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"Institute of Science and Technology Austria","status":"public","doi":"10.15479/AT-ISTA-19540","OA_place":"publisher","publication_status":"published","citation":{"short":"S.J. Henheik, Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems, Institute of Science and Technology Austria, 2025.","ieee":"S. J. Henheik, “Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems,” Institute of Science and Technology Austria, 2025.","chicago":"Henheik, Sven Joscha. “Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-19540\">https://doi.org/10.15479/AT-ISTA-19540</a>.","apa":"Henheik, S. J. (2025). <i>Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-19540\">https://doi.org/10.15479/AT-ISTA-19540</a>","ama":"Henheik SJ. Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-19540\">10.15479/AT-ISTA-19540</a>","mla":"Henheik, Sven Joscha. <i>Modeling Complex Quantum Systems: Random Matrices, BCS Theory, and Quantum Lattice Systems</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-19540\">10.15479/AT-ISTA-19540</a>.","ista":"Henheik SJ. 2025. Modeling complex quantum systems: Random matrices, BCS theory, and quantum lattice systems. Institute of Science and Technology Austria."},"year":"2025","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"status":"public","id":"14343","relation":"part_of_dissertation"},{"id":"13317","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"11732","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"12184","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"14421"},{"relation":"part_of_dissertation","id":"10623","status":"public"},{"status":"public","id":"18112","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"19001","status":"public"},{"relation":"part_of_dissertation","id":"10642","status":"public"},{"relation":"part_of_dissertation","id":"19545","status":"public"},{"relation":"part_of_dissertation","id":"19546","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"19550"},{"status":"public","id":"19551","relation":"part_of_dissertation"},{"status":"public","id":"19552","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"19547"},{"relation":"part_of_dissertation","id":"19548","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"14542"},{"relation":"part_of_dissertation","status":"public","id":"18656"},{"relation":"part_of_dissertation","id":"17049","status":"public"},{"id":"18764","status":"public","relation":"part_of_dissertation"}]},"oa":1,"date_updated":"2026-10-16T08:41:47Z","file":[{"file_name":"Henheik-Thesis_source_final.zip","creator":"shenheik","date_updated":"2025-04-10T21:14:18Z","file_id":"19542","access_level":"closed","date_created":"2025-04-10T21:14:18Z","content_type":"application/zip","checksum":"b8477ae5578436c72c3bb4193ad34ac5","file_size":4107587,"relation":"source_file"},{"checksum":"e9fc0ea12ec46c9f71110c33217c4140","file_size":9999492,"relation":"main_file","access_level":"open_access","date_created":"2025-04-11T13:16:05Z","content_type":"application/pdf","success":1,"file_id":"19553","date_updated":"2025-04-11T13:16:05Z","file_name":"Henheik-Thesis-pdfa_FINAL.pdf","creator":"shenheik"},{"file_id":"19615","date_updated":"2025-04-23T14:10:27Z","file_name":"Henheik-Thesis-Volume1_print.pdf","creator":"cchlebak","checksum":"f94580f86c785e7108eb116cd189e225","file_size":13276442,"relation":"other","access_level":"closed","date_created":"2025-04-23T14:10:27Z","content_type":"application/pdf"},{"access_level":"closed","content_type":"application/pdf","date_created":"2025-04-23T14:11:05Z","checksum":"b927ead3c78020ffb32918911deedb74","file_size":7628767,"relation":"other","creator":"cchlebak","file_name":"Henheik-Thesis-Volume2_print.pdf","file_id":"19616","date_updated":"2025-04-23T14:11:05Z"}],"oa_version":"Published Version","file_date_updated":"2025-04-23T14:11:05Z","_id":"19540","ec_funded":1,"month":"04","date_created":"2025-04-10T21:21:18Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"type":"dissertation","article_processing_charge":"No","day":"10","publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-057-2"]},"doi_confirm":"1","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"}],"page":"720","corr_author":"1","language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"date_published":"2025-04-10T00:00:00Z","has_accepted_license":"1","fulldoi":"https://doi.org/10.15479/AT-ISTA-19540","degree_awarded":"PhD","ddc":["519"]},{"related_material":{"record":[{"relation":"earlier_version","id":"17174","status":"public"},{"relation":"dissertation_contains","id":"20575","status":"public"},{"relation":"dissertation_contains","status":"public","id":"19540"}]},"das_tickbox":"0","file":[{"creator":"dernst","file_name":"2025_AnnalesHenriPoincare_Erdoes.pdf","success":1,"date_updated":"2025-06-25T05:38:34Z","file_id":"19895","date_created":"2025-06-25T05:38:34Z","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_size":977773,"checksum":"49e6a934db540206f7eaa0c798553ded"}],"isi":1,"date_updated":"2026-10-16T08:41:47Z","oa":1,"publication":"Annales Henri Poincare","oa_version":"Published Version","file_date_updated":"2025-06-25T05:38:34Z","intvolume":"        26","ec_funded":1,"_id":"18764","month":"06","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2025-01-05T23:01:59Z","department":[{"_id":"LaEr"}],"article_type":"original","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).","title":"Prethermalization for deformed Wigner matrices","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"}],"quality_controlled":"1","status":"public","publisher":"Springer Nature","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"doi":"10.1007/s00023-024-01518-y","OA_type":"hybrid","publication_status":"published","OA_place":"publisher","citation":{"chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” <i>Annales Henri Poincare</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00023-024-01518-y\">https://doi.org/10.1007/s00023-024-01518-y</a>.","apa":"Erdös, L., Henheik, S. J., Reker, J., &#38; Riabov, V. (2025). Prethermalization for deformed Wigner matrices. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-024-01518-y\">https://doi.org/10.1007/s00023-024-01518-y</a>","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025) 1991–2033.","ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner matrices,” <i>Annales Henri Poincare</i>, vol. 26. Springer Nature, pp. 1991–2033, 2025.","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. <i>Annales Henri Poincare</i>. 2025;26:1991-2033. doi:<a href=\"https://doi.org/10.1007/s00023-024-01518-y\">10.1007/s00023-024-01518-y</a>","mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” <i>Annales Henri Poincare</i>, vol. 26, Springer Nature, 2025, pp. 1991–2033, doi:<a href=\"https://doi.org/10.1007/s00023-024-01518-y\">10.1007/s00023-024-01518-y</a>."},"volume":26,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2025","researchdata_availability":"no","language":[{"iso":"eng"}],"date_published":"2025-06-01T00:00:00Z","external_id":{"arxiv":["2310.06677"],"isi":["001385326500001"]},"arxiv":1,"has_accepted_license":"1","ddc":["510"],"fulldoi":"https://doi.org/10.1007/s00023-024-01518-y","type":"journal_article","article_processing_charge":"Yes (via OA deal)","day":"01","publication_identifier":{"issn":["1424-0637"]},"scopus_import":"1","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","full_name":"Reker, Jana"},{"full_name":"Riabov, Volodymyr","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov"}],"page":"1991-2033","corr_author":"1","supplementarymaterial":"yes"},{"day":"17","article_processing_charge":"No","type":"preprint","corr_author":"1","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.05488","open_access":"1"}],"arxiv":1,"external_id":{"arxiv":["2309.05488"]},"date_published":"2024-12-17T00:00:00Z","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.48550/arXiv.2309.05488","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"status":"public","title":"Eigenstate thermalisation at the edge for Wigner matrices","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling."}],"acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2024","citation":{"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>","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. .","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>.","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>"},"OA_place":"repository","publication_status":"draft","doi":"10.48550/arXiv.2309.05488","oa_version":"Preprint","publication":"arXiv","oa":1,"date_updated":"2026-07-29T13:18:16Z","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"department":[{"_id":"LaEr"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2025-04-11T08:19:22Z","month":"12","ec_funded":1,"_id":"19545"},{"doi":"10.48550/arXiv.2409.17297","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.17297"}],"author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"full_name":"Langmann, Edwin","first_name":"Edwin","last_name":"Langmann"},{"orcid":"0000-0003-4476-2288","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"citation":{"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>.","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>","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","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>.","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>","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>."},"publication_status":"draft","corr_author":"1","OA_place":"repository","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2024","type":"preprint","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band superconductor the effect of inter-band coupling can only increase\r\nthe critical temperature, irrespective of its attractive or repulsive nature\r\nand its strength. Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the dependence of the increase in critical temperature on the\r\ninter-band coupling is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands, or (2) quadratic, if there is only one dominating band."}],"title":"Multi-band superconductors have enhanced critical temperatures","day":"21","status":"public","_id":"19550","fulldoi":"https://doi.org/10.48550/arXiv.2409.17297","month":"10","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2025-04-11T11:43:58Z","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"related_material":{"record":[{"relation":"later_version","id":"22290","status":"public"},{"status":"public","id":"19540","relation":"dissertation_contains"}]},"oa":1,"language":[{"iso":"eng"}],"date_updated":"2026-07-29T13:18:16Z","date_published":"2024-10-21T00:00:00Z","external_id":{"arxiv":["2409.17297"]},"oa_version":"Preprint","publication":"arXiv","arxiv":1},{"day":"03","article_processing_charge":"No","type":"preprint","corr_author":"1","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László"},{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr","full_name":"Riabov, Volodymyr"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.06813","open_access":"1"}],"arxiv":1,"external_id":{"arxiv":["2410.06813"]},"date_published":"2024-11-03T00:00:00Z","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.48550/arXiv.2410.06813","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"status":"public","abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes.","lang":"eng"}],"title":"Cusp universality for correlated random matrices","acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","year":"2024","OA_place":"repository","citation":{"chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>.","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>","short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","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>.","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>."},"publication_status":"draft","doi":"10.48550/arXiv.2410.06813","oa_version":"Preprint","publication":"arXiv","oa":1,"date_updated":"2026-07-29T13:18:17Z","related_material":{"record":[{"status":"public","id":"20322","relation":"later_version"},{"id":"20575","status":"public","relation":"dissertation_contains"},{"status":"public","id":"19540","relation":"dissertation_contains"}]},"department":[{"_id":"LaEr"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2025-04-11T08:48:21Z","month":"11","ec_funded":1,"_id":"19547"},{"month":"10","fulldoi":"https://doi.org/10.48550/arXiv.2410.10809","_id":"19551","department":[{"_id":"LaEr"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2025-04-11T11:54:56Z","oa":1,"language":[{"iso":"eng"}],"date_updated":"2026-07-29T13:18:16Z","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"arxiv":1,"external_id":{"arxiv":["2410.10809"]},"date_published":"2024-10-14T00:00:00Z","publication":"arXiv","oa_version":"Preprint","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Wessel","first_name":"Tom","full_name":"Wessel, Tom"}],"doi":"10.48550/arXiv.2410.10809","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.10809"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2024","OA_place":"repository","corr_author":"1","citation":{"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>. .","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>.","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>","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>","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>.","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>."},"publication_status":"draft","title":"Response theory for locally gapped systems","abstract":[{"lang":"eng","text":"We introduce a notion of a \\emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings.\r\nOn a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system.\r\nMore precisely, we say that an equilibrium state ρ0 of a Hamiltonian H0 is locally gapped in Λgap⊂Λ, whenever the Liouvillian −i[H0,⋅] is almost invertible on local observables supported in Λgap when tested in ρ0.\r\nTo put this into context, we provide other alternative notions of a local gap and discuss their relations.\r\nThe validity of response theory is based on the construction of \\emph{non-equilibrium almost stationary states} (NEASSs).\r\nBy controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \\(\\epsilon V\\) acts in a region which is further than |logϵ| away from the non-gapped region Λ∖Λgap."}],"article_processing_charge":"No","type":"preprint","day":"14","status":"public"},{"OA_type":"green","doi":"10.1142/s2010326324500072","researchdata_availability":"unclear","volume":13,"year":"2024","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.","short":"G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (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>","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>.","mla":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>, vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>.","ama":"Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. 2024;13(2). doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>","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."},"OA_place":"repository","publication_status":"published","abstract":[{"lang":"eng","text":"We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random matrix models."}],"title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"publisher":"World Scientific Publishing","issue":"2","status":"public","quality_controlled":"1","month":"04","ec_funded":1,"_id":"17047","article_type":"original","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2024-05-23T08:31:57Z","oa":1,"date_updated":"2026-10-02T11:31:29Z","isi":1,"related_material":{"record":[{"id":"17164","status":"public","relation":"dissertation_contains"}]},"das_tickbox":"0","intvolume":"        13","publication":"Random Matrices: Theory and Applications","oa_version":"Preprint","author":[{"orcid":"0000-0001-6892-8137","last_name":"Dubach","full_name":"Dubach, Guillaume","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","last_name":"Reker"}],"scopus_import":"1","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2212.14638"}],"supplementarymaterial":"unclear","article_number":"2450007","corr_author":"1","article_processing_charge":"No","type":"journal_article","day":"01","fulldoi":"https://doi.org/10.1142/s2010326324500072","language":[{"iso":"eng"}],"arxiv":1,"external_id":{"isi":["001229295200002"],"arxiv":["2212.14638"]},"date_published":"2024-04-01T00:00:00Z"},{"date_created":"2023-11-15T23:48:14Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"article_type":"original","ec_funded":1,"_id":"14542","month":"10","oa_version":"Published Version","publication":"Reviews in Mathematical Physics","file_date_updated":"2025-01-09T07:56:28Z","intvolume":"        36","related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"},{"relation":"dissertation_contains","id":"18135","status":"public"}]},"das_tickbox":"0","file":[{"success":1,"date_updated":"2025-01-09T07:56:28Z","file_id":"18786","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","creator":"dernst","checksum":"2b053a4223b4db14b90520999ec56054","file_size":503910,"relation":"main_file","access_level":"open_access","date_created":"2025-01-09T07:56:28Z","content_type":"application/pdf"}],"isi":1,"date_updated":"2026-10-02T11:43:00Z","oa":1,"OA_place":"publisher","publication_status":"published","citation":{"ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <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>.","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>","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>","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>.","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.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024)."},"volume":36,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"researchdata_availability":"no","year":"2024","doi":"10.1142/s0129055x2360005x","OA_type":"hybrid","quality_controlled":"1","issue":"9","status":"public","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity"}],"publisher":"World Scientific Publishing","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.","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"}],"title":"Universality in low-dimensional BCS theory","has_accepted_license":"1","ddc":["510"],"fulldoi":"https://doi.org/10.1142/s0129055x2360005x","external_id":{"arxiv":["2301.05621"],"isi":["001099640300002"]},"date_published":"2024-10-01T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"corr_author":"1","article_number":"2360005 ","supplementarymaterial":"no","scopus_import":"1","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"},{"orcid":"0000-0003-4476-2288","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard"},{"last_name":"Roos","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","full_name":"Roos, Barbara"}],"day":"01","type":"journal_article","article_processing_charge":"Yes (in subscription journal)"},{"doi":"10.1007/s00220-024-05143-y","OA_type":"hybrid","citation":{"short":"L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).","ieee":"L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12. Springer Nature, 2024.","chicago":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>.","apa":"Erdös, L., &#38; Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>","ama":"Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. 2024;405(12). doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>","mla":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12, 282, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>.","ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282."},"publication_status":"published","OA_place":"publisher","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2024","volume":405,"researchdata_availability":"not applicable","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure."}],"quality_controlled":"1","publisher":"Springer Nature","status":"public","issue":"12","_id":"18554","month":"12","dataavailabilitystatement":"There is no data associated to this work.","date_created":"2024-11-17T23:01:46Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","department":[{"_id":"LaEr"}],"das_tickbox":"1","related_material":{"record":[{"id":"20575","status":"public","relation":"dissertation_contains"}]},"oa":1,"date_updated":"2026-10-16T08:34:30Z","isi":1,"file":[{"file_id":"18562","date_updated":"2024-11-18T08:15:07Z","success":1,"file_name":"2024_CommMathPhysics_Erdoes.pdf","creator":"dernst","checksum":"c9ae0ea195bd39b8b3a630d492fb00dc","file_size":1426046,"relation":"main_file","access_level":"open_access","content_type":"application/pdf","date_created":"2024-11-18T08:15:07Z"}],"publication":"Communications in Mathematical Physics","oa_version":"Published Version","intvolume":"       405","file_date_updated":"2024-11-18T08:15:07Z","scopus_import":"1","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr"}],"article_number":"282","corr_author":"1","supplementarymaterial":"yes","type":"journal_article","article_processing_charge":"Yes (via OA deal)","day":"01","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s00220-024-05143-y","ddc":["510"],"language":[{"iso":"eng"}],"pmid":1,"external_id":{"isi":["001348943900004"],"pmid":["39526190"],"arxiv":["2403.10359"]},"date_published":"2024-12-01T00:00:00Z","arxiv":1},{"_id":"13975","month":"03","dataavailabilitystatement":"All data generated or analyzed during this study are included in this published article.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2023-08-06T22:01:13Z","article_type":"original","department":[{"_id":"LaEr"}],"das_tickbox":"1","oa":1,"date_updated":"2026-10-16T08:30:34Z","isi":1,"file":[{"file_name":"2024_JourTheorProbab_Campbell.pdf","creator":"dernst","file_id":"17300","date_updated":"2024-07-22T09:41:21Z","success":1,"access_level":"open_access","content_type":"application/pdf","date_created":"2024-07-22T09:41:21Z","file_size":555070,"checksum":"f7793d313104c70422140c5e6494c779","relation":"main_file"}],"publication":"Journal of Theoretical Probability","oa_version":"Published Version","intvolume":"        37","file_date_updated":"2024-07-22T09:41:21Z","doi":"10.1007/s10959-023-01275-4","citation":{"ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. 2024;37:933-973. doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>, vol. 37, Springer Nature, 2024, pp. 933–73, doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>.","ista":"Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 37, 933–973.","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973.","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” <i>Journal of Theoretical Probability</i>, vol. 37. Springer Nature, pp. 933–973, 2024.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>.","apa":"Campbell, A. J., &#38; O’Rourke, S. (2024). Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>"},"publication_status":"published","volume":37,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2024","researchdata_availability":"yes (supplementary data)","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).","abstract":[{"lang":"eng","text":"We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln  converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure."}],"title":"Spectrum of Lévy–Khintchine random laplacian matrices","quality_controlled":"1","publisher":"Springer Nature","status":"public","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s10959-023-01275-4","ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"date_published":"2024-03-01T00:00:00Z","arxiv":1,"publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]},"scopus_import":"1","author":[{"last_name":"Campbell","full_name":"Campbell, Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J"},{"last_name":"O’Rourke","full_name":"O’Rourke, Sean","first_name":"Sean"}],"page":"933-973","corr_author":"1","supplementarymaterial":"yes","type":"journal_article","article_processing_charge":"Yes (via OA deal)","day":"01"},{"month":"07","_id":"17281","department":[{"_id":"LaEr"}],"article_type":"original","date_created":"2024-07-21T22:01:01Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"file":[{"creator":"dernst","file_name":"2024_IMRN_Campbell.pdf","success":1,"file_id":"17288","date_updated":"2024-07-22T06:40:19Z","access_level":"open_access","date_created":"2024-07-22T06:40:19Z","content_type":"application/pdf","file_size":1233508,"checksum":"f36a7dbf53f23d5833db711052e69b49","relation":"main_file"}],"date_updated":"2026-10-16T08:32:45Z","oa":1,"das_tickbox":"0","file_date_updated":"2024-07-22T06:40:19Z","intvolume":"      2024","publication":"International Mathematics Research Notices","oa_version":"Published Version","doi":"10.1093/imrn/rnae062","volume":2024,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"researchdata_availability":"no","year":"2024","publication_status":"published","citation":{"ista":"Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024(13), 10189–10218.","mla":"Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>.","ama":"Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. 2024;2024(13):10189-10218. doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>","apa":"Campbell, A. J., O’Rourke, S., &#38; Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>","chicago":"Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>.","ieee":"A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218."},"title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","abstract":[{"text":"We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions.","lang":"eng"}],"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.","issue":"13","status":"public","publisher":"Oxford University Press","quality_controlled":"1","ddc":["510"],"fulldoi":"https://doi.org/10.1093/imrn/rnae062","has_accepted_license":"1","language":[{"iso":"eng"}],"date_published":"2024-07-01T00:00:00Z","external_id":{"isi":["001198019500001"]},"author":[{"full_name":"Campbell, Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J","last_name":"Campbell"},{"last_name":"O'Rourke","first_name":"Sean","full_name":"O'Rourke, Sean"},{"full_name":"Renfrew, David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","first_name":"David T","last_name":"Renfrew","orcid":"0000-0003-3493-121X"}],"scopus_import":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"supplementarymaterial":"yes","page":"10189-10218","corr_author":"1","article_processing_charge":"Yes (via OA deal)","type":"journal_article","day":"01"}]