{"title":"一般线性群上随机游走系数的一个局部极限定理和不变测度的一个0 - 1定律","authors":"I. Grama, Jean-François Quint, Hui Xiao","doi":"10.1214/21-aihp1221","DOIUrl":null,"url":null,"abstract":"We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg [13] and Guivarc'h and Le Page [20]. As an application, we establish a local limit theorem for the coefficients of random walks on the general linear group.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"4 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group\",\"authors\":\"I. Grama, Jean-François Quint, Hui Xiao\",\"doi\":\"10.1214/21-aihp1221\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg [13] and Guivarc'h and Le Page [20]. As an application, we establish a local limit theorem for the coefficients of random walks on the general linear group.\",\"PeriodicalId\":42884,\"journal\":{\"name\":\"Annales de l Institut Henri Poincare D\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2020-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de l Institut Henri Poincare D\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/21-aihp1221\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/21-aihp1221","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 10
摘要
推广了Furstenberg[13]和Guivarc'h and Le Page[20]的结果，证明了代数集平稳测度的一个0 - 1定律。作为应用，我们建立了一般线性群上随机游走系数的局部极限定理。
A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group
We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg [13] and Guivarc'h and Le Page [20]. As an application, we establish a local limit theorem for the coefficients of random walks on the general linear group.
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