{"title":"某些相关可解李群的泊松边界的显式描述","authors":"Christophe Cuny","doi":"10.1016/S0764-4442(01)02121-8","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>G</em> be a connected solvable Lie group with abelian derived group and <em>μ</em> be a spread out probability measure on <em>G</em>. We give an explicit description of the Poisson boundary in terms of almost sure convergence of the right random walk of law <em>μ</em>. We characterize the Poisson boundary by an integral criterion for some matricial groups.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 741-744"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02121-8","citationCount":"1","resultStr":"{\"title\":\"Description explicite de la frontière de Poisson pour certains groupes de Lie résolubles connexes\",\"authors\":\"Christophe Cuny\",\"doi\":\"10.1016/S0764-4442(01)02121-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>G</em> be a connected solvable Lie group with abelian derived group and <em>μ</em> be a spread out probability measure on <em>G</em>. We give an explicit description of the Poisson boundary in terms of almost sure convergence of the right random walk of law <em>μ</em>. We characterize the Poisson boundary by an integral criterion for some matricial groups.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 8\",\"pages\":\"Pages 741-744\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02121-8\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021218\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021218","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Description explicite de la frontière de Poisson pour certains groupes de Lie résolubles connexes
Let G be a connected solvable Lie group with abelian derived group and μ be a spread out probability measure on G. We give an explicit description of the Poisson boundary in terms of almost sure convergence of the right random walk of law μ. We characterize the Poisson boundary by an integral criterion for some matricial groups.
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