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arXiv · 1909.06866

Decomposition of random walk measures on the one-dimensional torus

Tom Gilat
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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 $μ_1$ has the property that the random walk with initial distribution $μ_1$ evolved by the action of $S$ equidistributes very fast. The second measure $μ_2$ in the decomposition is concentrated on very small neighborhoods of a small number of points.

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Tom Gilat. 2020-03-04. Decomposition of random walk measures on the one-dimensional torus. https://doi.org/10.19086/da.11888

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