{"department":[{"_id":"LaEr"}],"oa":1,"abstract":[{"text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices.","lang":"eng"}],"ec_funded":1,"date_published":"2023-02-08T00:00:00Z","oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","file":[{"relation":"main_file","file_name":"2023_ElectCommProbability_Dubach.pdf","content_type":"application/pdf","file_size":479105,"date_created":"2023-02-27T09:43:27Z","date_updated":"2023-02-27T09:43:27Z","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","creator":"dernst","access_level":"open_access","success":1,"file_id":"12692"}],"article_type":"original","publisher":"Institute of Mathematical Statistics","page":"1-13","day":"08","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"intvolume":"        28","file_date_updated":"2023-02-27T09:43:27Z","publication_identifier":{"eissn":["1083-589X"]},"date_created":"2023-02-26T23:01:01Z","language":[{"iso":"eng"}],"article_processing_charge":"No","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","status":"public","acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","isi":1,"publication_status":"published","volume":28,"ddc":["510"],"scopus_import":"1","month":"02","publication":"Electronic Communications in Probability","citation":{"ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023."},"year":"2023","_id":"12683","doi":"10.1214/23-ECP516","quality_controlled":"1","external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"author":[{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","last_name":"Dubach","full_name":"Dubach, Guillaume"},{"full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603"}],"has_accepted_license":"1","date_updated":"2023-10-17T12:48:10Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}