{"title":"Dynamics of a rank-one perturbation of a Hermitian matrix","quality_controlled":"1","status":"public","oa_version":"Published Version","oa":1,"date_created":"2023-02-26T23:01:01Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","scopus_import":"1","date_published":"2023-02-08T00:00:00Z","publication_status":"published","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","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."}],"type":"journal_article","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"file_name":"2023_ElectCommProbability_Dubach.pdf","creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","file_size":479105,"date_created":"2023-02-27T09:43:27Z","file_id":"12692","success":1,"date_updated":"2023-02-27T09:43:27Z"}],"day":"08","article_processing_charge":"No","month":"02","date_updated":"2023-10-17T12:48:10Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"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.","file_date_updated":"2023-02-27T09:43:27Z","isi":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"ddc":["510"],"intvolume":"        28","volume":28,"year":"2023","citation":{"short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","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>","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>.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 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.","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>."},"article_type":"original","ec_funded":1,"_id":"12683","language":[{"iso":"eng"}],"has_accepted_license":"1","author":[{"orcid":"0000-0001-6892-8137","last_name":"Dubach","first_name":"Guillaume","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"publication":"Electronic Communications in Probability","doi":"10.1214/23-ECP516","page":"1-13","external_id":{"arxiv":["2108.13694"],"isi":["000950650200005"]},"publication_identifier":{"eissn":["1083-589X"]}}