{"status":"public","date_updated":"2025-07-10T11:51:54Z","arxiv":1,"language":[{"iso":"eng"}],"OA_place":"repository","_id":"19546","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10718","open_access":"1"}],"department":[{"_id":"LaEr"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"oa_version":"Preprint","type":"preprint","ec_funded":1,"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Kolupaiev","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii"}],"oa":1,"abstract":[{"lang":"eng","text":"We study the sensitivity of the eigenvectors of random matrices, showing that\r\neven small perturbations make the eigenvectors almost orthogonal. More\r\nprecisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show\r\nthat their bulk eigenvectors become asymptotically orthogonal as soon as\r\n$\\mathrm{Tr}(D_1-D_2)^2\\gg 1$, or their respective energies are separated on a\r\nscale much bigger than the local eigenvalue spacing. Furthermore, we show that\r\nquadratic forms of eigenvectors of $W+D_1$, $W+D_2$ with any deterministic\r\nmatrix $A\\in\\mathbf{C}^{N\\times N}$ in a specific subspace of codimension one\r\nare of size $N^{-1/2}$. This proves a generalization of the Eigenstate\r\nThermalization Hypothesis to eigenvectors belonging to two different spectral\r\nfamilies."}],"acknowledgement":"Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).","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>.","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>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>arXiv</i>. .","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>.","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>","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>."},"day":"30","title":"Eigenvector decorrelation for random matrices","date_published":"2025-01-30T00:00:00Z","corr_author":"1","publication":"arXiv","publication_status":"draft","month":"01","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","doi":"10.48550/arXiv.2410.10718","article_processing_charge":"No","date_created":"2025-04-11T08:34:49Z","year":"2025","external_id":{"arxiv":["2410.10718"]},"license":"https://creativecommons.org/licenses/by/4.0/"}