[{"language":[{"iso":"eng"}],"file_date_updated":"2025-02-05T07:01:40Z","OA_type":"hybrid","date_published":"2025-01-30T00:00:00Z","pmid":1,"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"title":"Loschmidt echo for deformed Wigner matrices","article_processing_charge":"Yes (via OA deal)","intvolume":"       115","has_accepted_license":"1","type":"journal_article","_id":"19001","year":"2025","date_updated":"2026-04-07T12:37:10Z","publication":"Letters in Mathematical Physics","date_created":"2025-02-05T06:48:29Z","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.","arxiv":1,"publication_identifier":{"issn":["1573-0530"]},"external_id":{"arxiv":["2410.08108"],"isi":["001409618800002"],"pmid":["39896265"]},"abstract":[{"text":"We consider two Hamiltonians that are close to each other, H1≈H2, and analyze the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2 that expresses the effect of an imperfect time reversal on the initial state ψ0. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such H1 and H2.","lang":"eng"}],"department":[{"_id":"LaEr"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","license":"https://creativecommons.org/licenses/by/4.0/","OA_place":"publisher","doi":"10.1007/s11005-025-01904-5","quality_controlled":"1","oa_version":"Published Version","article_type":"original","month":"01","article_number":"14","ddc":["510"],"status":"public","publication_status":"published","citation":{"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>","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>","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>.","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>.","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."},"isi":1,"file":[{"date_updated":"2025-02-05T07:01:40Z","file_id":"19004","date_created":"2025-02-05T07:01:40Z","content_type":"application/pdf","relation":"main_file","file_size":828335,"access_level":"open_access","file_name":"2025_LettersMathPhysics_Erdoes.pdf","success":1,"checksum":"ee07edf5f85a6f2651926b2f8760af74","creator":"dernst"}],"scopus_import":"1","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"day":"30","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii"}],"volume":115,"publisher":"Springer Nature","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}]},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"orcid":"0000-0003-1491-4623","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii"}],"day":"30","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"ec_funded":1,"citation":{"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>","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. arXiv, <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>.","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>.","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>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>arXiv</i>. ."},"publication_status":"draft","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10718","open_access":"1"}],"status":"public","month":"01","oa_version":"Preprint","doi":"10.48550/arXiv.2410.10718","OA_place":"repository","corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"department":[{"_id":"LaEr"}],"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"}],"external_id":{"arxiv":["2410.10718"]},"arxiv":1,"acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","publication":"arXiv","date_created":"2025-04-11T08:34:49Z","date_updated":"2026-04-07T12:37:11Z","year":"2025","type":"preprint","_id":"19546","title":"Eigenvector decorrelation for random matrices","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2025-01-30T00:00:00Z","language":[{"iso":"eng"}]},{"day":"20","author":[{"full_name":"Bao, Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","orcid":"0000-0003-1491-4623"}],"publisher":"Springer Nature","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"publication_status":"epub_ahead","citation":{"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.","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.","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>.","short":"Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025).","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>"},"isi":1,"scopus_import":"1","ec_funded":1,"oa_version":"Published Version","article_type":"original","month":"09","ddc":["500"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-025-01422-4"}],"status":"public","OA_place":"publisher","quality_controlled":"1","doi":"10.1007/s00440-025-01422-4","department":[{"_id":"LaEr"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","year":"2025","date_updated":"2026-06-18T18:23:40Z","date_created":"2025-10-16T13:10:26Z","publication":"Probability Theory and Related Fields","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.","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"arxiv":1,"external_id":{"arxiv":["2503.06549"],"isi":["001574640900001"]},"PlanS_conform":"1","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"}],"type":"journal_article","_id":"20478","language":[{"iso":"eng"}],"OA_type":"hybrid","date_published":"2025-09-20T00:00:00Z","title":"Decorrelation transition in the Wigner minor process","article_processing_charge":"Yes (via OA deal)"},{"department":[{"_id":"LaEr"},{"_id":"GradSch"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.","publication_identifier":{"eissn":["2050-5094"]},"arxiv":1,"year":"2023","date_updated":"2026-04-07T12:37:10Z","publication":"Forum of Mathematics, Sigma","date_created":"2023-09-17T22:01:09Z","abstract":[{"text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.","lang":"eng"}],"external_id":{"arxiv":["2301.05181"],"isi":["001051980200001"]},"intvolume":"        11","_id":"14343","type":"journal_article","has_accepted_license":"1","language":[{"iso":"eng"}],"file_date_updated":"2023-09-20T11:09:35Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_processing_charge":"Yes","title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","date_published":"2023-08-23T00:00:00Z","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X"},{"full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","first_name":"Oleksii","orcid":"0000-0003-1491-4623"}],"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"day":"23","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publisher":"Cambridge University Press","volume":11,"isi":1,"file":[{"relation":"main_file","file_size":852652,"access_level":"open_access","file_name":"2023_ForumMathematics_Cipolloni.pdf","date_created":"2023-09-20T11:09:35Z","file_id":"14352","date_updated":"2023-09-20T11:09:35Z","content_type":"application/pdf","creator":"dernst","success":1,"checksum":"eb747420e6a88a7796fa934151957676"}],"citation":{"mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e74, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023."},"publication_status":"published","ec_funded":1,"scopus_import":"1","article_type":"original","month":"08","oa_version":"Published Version","status":"public","article_number":"e74","ddc":["510"],"quality_controlled":"1","doi":"10.1017/fms.2023.70"}]