{"title":"Law of large numbers for the spectral radius of random matrix products","authors":"Richard Aoun, Cagri Sert","doi":"10.1353/AJM.2021.0025","DOIUrl":null,"url":null,"abstract":"abstract:We prove that the spectral radius of an i.i.d. random walk on ${\\rm GL}_d(\\Bbb{C})$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/AJM.2021.0025","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/AJM.2021.0025","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 10
Abstract
abstract:We prove that the spectral radius of an i.i.d. random walk on ${\rm GL}_d(\Bbb{C})$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed.
期刊介绍：
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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