{"volume":36,"das_tickbox":"0","year":"2026","publisher":"Institute of Mathematical Statistics","date_updated":"2026-09-16T10:00:54Z","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"full_name":"Kolupaiev, Oleksii","last_name":"Kolupaiev","orcid":"0000-0003-1491-4623","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"OA_place":"repository","scopus_import":"1","supplementarymaterial":"yes","publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"corr_author":"1","researchdata_availability":"no","oa_version":"Preprint","acknowledgement":"L. Erdős, J. Henheik and O. Kolupaiev were supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. G. Cipolloni is partially supported by the MUR Excellence Department Project MatMod@TOV awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.","arxiv":1,"language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1214/26-AAP2318","abstract":[{"text":"We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two deformed Wigner matrices 𝑊 +𝐷1, 𝑊 +𝐷2 and show that their bulk eigenvectors become asymptotically orthogonal as soon as Tr⁡(𝐷1−𝐷2)2 ≫1, or their respective energies are separated on a scale much bigger than the local eigenvalue spacing. Furthermore, we show that quadratic forms of eigenvectors of 𝑊 +𝐷1, 𝑊 +𝐷2 with any deterministic matrix 𝐴 ∈𝐂𝑁×𝑁 in a specific subspace of codimension one are of size 𝑁−1/2. This proves a generalization of the eigenstate thermalization hypothesis to eigenvectors belonging to two different spectral families.","lang":"eng"}],"department":[{"_id":"LaEr"},{"_id":"GradSch"}],"date_published":"2026-08-01T00:00:00Z","external_id":{"arxiv":["2410.10718"]},"article_processing_charge":"No","intvolume":"        36","doi":"10.1214/26-AAP2318","ec_funded":1,"page":"3707-3756","issue":"4","type":"journal_article","citation":{"ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2026. Eigenvector decorrelation for random matrices. Annals of Applied Probability. 36(4), 3707–3756.","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. <i>Annals of Applied Probability</i>. 2026;36(4):3707-3756. doi:<a href=\"https://doi.org/10.1214/26-AAP2318\">10.1214/26-AAP2318</a>","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2026. <a href=\"https://doi.org/10.1214/26-AAP2318\">https://doi.org/10.1214/26-AAP2318</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Annals of Applied Probability 36 (2026) 3707–3756.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2026). Eigenvector decorrelation for random matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/26-AAP2318\">https://doi.org/10.1214/26-AAP2318</a>","mla":"Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” <i>Annals of Applied Probability</i>, vol. 36, no. 4, Institute of Mathematical Statistics, 2026, pp. 3707–56, doi:<a href=\"https://doi.org/10.1214/26-AAP2318\">10.1214/26-AAP2318</a>.","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>Annals of Applied Probability</i>, vol. 36, no. 4. Institute of Mathematical Statistics, pp. 3707–3756, 2026."},"month":"08","status":"public","OA_type":"green","oa":1,"article_type":"original","quality_controlled":"1","related_material":{"record":[{"status":"public","id":"19546","relation":"earlier_version"}]},"day":"01","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"publication":"Annals of Applied Probability","_id":"22923","mathsc":["60B20","82C10"],"date_created":"2026-09-13T22:01:54Z","keyword":["characteristic flow","Davis–Kahan theorem","Eigenstate thermalization","Eigenvector perturbation theory","Local law","zigzag strategy"],"title":"Eigenvector decorrelation for random matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10718","open_access":"1"}]}