{"title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix","authors":"Guillaume Dubach, Jana Reker","doi":"10.1142/s2010326324500072","DOIUrl":null,"url":null,"abstract":"<p>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 <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>U</mi></math></span><span></span> that hold for a variety of unitary random matrix models.</p>","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Matrices-Theory and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s2010326324500072","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
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 that hold for a variety of unitary random matrix models.
期刊介绍：
Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics.
Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory.
Special issues devoted to single topic of current interest will also be considered and published in this journal.
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