Arijit Chakrabarty, Rajat Subhra Hazra, Moumanti Podder
{"title":"Largest eigenvalue of positive mean Gaussian matrices","authors":"Arijit Chakrabarty, Rajat Subhra Hazra, Moumanti Podder","doi":"arxiv-2409.05858","DOIUrl":null,"url":null,"abstract":"This short note studies the fluctuations of the largest eigenvalue of\nsymmetric random matrices with correlated Gaussian entries having positive\nmean. Under the assumption that the covariance kernel is absolutely summable,\nit is proved that the largest eigenvalue, after centering, converges in\ndistribution to normal with an explicitly defined mean and variance. This\nresult generalizes known findings for Wigner matrices with independent entries.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05858","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This short note studies the fluctuations of the largest eigenvalue of
symmetric random matrices with correlated Gaussian entries having positive
mean. Under the assumption that the covariance kernel is absolutely summable,
it is proved that the largest eigenvalue, after centering, converges in
distribution to normal with an explicitly defined mean and variance. This
result generalizes known findings for Wigner matrices with independent entries.