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

@article{Gilat2020DecompositionOR, title={Decomposition of random walk measures on the one-dimensional torus.}, author={Tom Gilat}, journal={discrete Analysis}, year={2020} }

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…

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