{"title":"Random normal matrices in the almost-circular regime","authors":"Sunggyu Byun, Seong-Mi Seo","doi":"10.3150/22-bej1514","DOIUrl":null,"url":null,"abstract":"We study random normal matrix models whose eigenvalues tend to be distributed within a narrow\"band\"around the unit circle of width proportional to $\\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials with various boundary conditions, we derive the scaling limits of the correlation functions, some of which appear in the previous literature notably in the context of almost-Hermitian random matrices. We also obtain that fluctuations of the maximal and minimal modulus of the ensembles follow the Gumbel or exponential law depending on the boundary conditions.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bernoulli","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3150/22-bej1514","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 13
Abstract
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow"band"around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials with various boundary conditions, we derive the scaling limits of the correlation functions, some of which appear in the previous literature notably in the context of almost-Hermitian random matrices. We also obtain that fluctuations of the maximal and minimal modulus of the ensembles follow the Gumbel or exponential law depending on the boundary conditions.
期刊介绍:
BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work.
BERNOULLI will publish:
Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed.
Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research:
Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments.
Scholarly written papers on some historical significant aspect of statistics and probability.