{"title":"一维环面上随机游动测度的分解。","authors":"T. Gilat","doi":"10.19086/da.11888","DOIUrl":null,"url":null,"abstract":"The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one $\\mu_1$ has the property that the random walk with initial distribution $\\mu_1$ evolved by the action of $S$ equidistributes very fast. The second measure $\\mu_2$ in the decomposition is concentrated on very small neighborhoods of a small number of points.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2019-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decomposition of random walk measures on the one-dimensional torus.\",\"authors\":\"T. Gilat\",\"doi\":\"10.19086/da.11888\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one $\\\\mu_1$ has the property that the random walk with initial distribution $\\\\mu_1$ evolved by the action of $S$ equidistributes very fast. The second measure $\\\\mu_2$ in the decomposition is concentrated on very small neighborhoods of a small number of points.\",\"PeriodicalId\":37312,\"journal\":{\"name\":\"Discrete Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2019-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.19086/da.11888\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19086/da.11888","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Decomposition of random walk measures on the one-dimensional torus.
The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one $\mu_1$ has the property that the random walk with initial distribution $\mu_1$ evolved by the action of $S$ equidistributes very fast. The second measure $\mu_2$ in the decomposition is concentrated on very small neighborhoods of a small number of points.
期刊介绍：
Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.
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