{"type":"journal_article","abstract":[{"lang":"eng","text":"We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random matrix models."}],"article_type":"original","article_processing_charge":"No","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"date_created":"2024-05-23T08:31:57Z","date_updated":"2024-07-04T11:20:30Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publication":"Random Matrices: Theory and Applications","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"month":"05","oa":1,"day":"21","author":[{"first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"first_name":"Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana"}],"publication_status":"epub_ahead","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2212.14638"}],"date_published":"2024-05-21T00:00:00Z","publisher":"World Scientific Publishing","language":[{"iso":"eng"}],"external_id":{"arxiv":["2212.14638"]},"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"17047","citation":{"ista":"Dubach G, Reker J. 2024. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications.","short":"G. Dubach, J. Reker, Random Matrices: Theory and Applications (2024).","ama":"Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. 2024. doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>","mla":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>.","apa":"Dubach, G., &#38; Reker, J. (2024). Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326324500072\">https://doi.org/10.1142/s2010326324500072</a>","ieee":"G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation of a unitary matrix,” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2024.","chicago":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s2010326324500072\">https://doi.org/10.1142/s2010326324500072</a>."},"doi":"10.1142/s2010326324500072","related_material":{"record":[{"id":"17164","relation":"dissertation_contains","status":"public"}]},"title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix","year":"2024","quality_controlled":"1","status":"public","oa_version":"Preprint"}