Decomposition of random walk measures on the one-dimensional torus.

IF 1 3区数学 Q1 MATHEMATICS Discrete Analysis Pub Date : 2019-09-15 DOI:10.19086/da.11888

T. Gilat

引用次数: 0

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.

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一维环面上随机游动测度的分解。

本文的主要结果是一维环面上测度的分解定理。给定一个足够大的正整数子集$S$，环面上的任意测度被分解为两个测度的和。第一个$\mu_1$的性质是初始分布$\mu_1$的随机游走由$S$的作用演变而来，平均分布非常快。分解中的第二个测度$\mu_2$集中在少量点的非常小的邻域上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

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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