{"corr_author":"1","date_updated":"2025-09-10T06:38:35Z","oa_version":"Published Version","quality_controlled":"1","oa":1,"title":"Optimal decay of eigenvector overlap for non-Hermitian random matrices","PlanS_conform":"1","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","last_name":"Xu","full_name":"Xu, Yuanyuan","orcid":"0000-0003-1559-1205","first_name":"Yuanyuan"}],"abstract":[{"lang":"eng","text":"We consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge."}],"has_accepted_license":"1","OA_type":"hybrid","year":"2025","department":[{"_id":"LaEr"}],"month":"09","main_file_link":[{"url":"https://doi.org/10.1016/j.jfa.2025.111180","open_access":"1"}],"ddc":["510"],"citation":{"mla":"Cipolloni, Giorgio, et al. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 290, no. 1, 111180, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">10.1016/j.jfa.2025.111180</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">https://doi.org/10.1016/j.jfa.2025.111180</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Xu, Y. (2025). Optimal decay of eigenvector overlap for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">https://doi.org/10.1016/j.jfa.2025.111180</a>","ista":"Cipolloni G, Erdös L, Xu Y. 2025. Optimal decay of eigenvector overlap for non-Hermitian random matrices. Journal of Functional Analysis. 290(1), 111180.","ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Optimal decay of eigenvector overlap for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 290, no. 1. Elsevier, 2025.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Functional Analysis 290 (2025).","ama":"Cipolloni G, Erdös L, Xu Y. Optimal decay of eigenvector overlap for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2025;290(1). doi:<a href=\"https://doi.org/10.1016/j.jfa.2025.111180\">10.1016/j.jfa.2025.111180</a>"},"scopus_import":"1","status":"public","language":[{"iso":"eng"}],"article_number":"111180","publication":"Journal of Functional Analysis","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       290","volume":290,"publication_identifier":{"issn":["0022-1236"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication_status":"epub_ahead","arxiv":1,"ec_funded":1,"publisher":"Elsevier","acknowledgement":"Partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Partially supported by National Key R&D Program of China No. 2024YFA1013503.","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_type":"original","date_published":"2025-09-09T00:00:00Z","type":"journal_article","date_created":"2025-09-10T05:46:07Z","day":"09","article_processing_charge":"Yes (via OA deal)","OA_place":"publisher","doi":"10.1016/j.jfa.2025.111180","external_id":{"arxiv":["2411.16572"]},"_id":"20328","issue":"1"}