Decomposition of random walk measures on the one-dimensional torus
Dynamical Systems
2020-03-05 v2 Combinatorics
Probability
Abstract
The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one has the property that the random walk with initial distribution evolved by the action of equidistributes very fast. The second measure in the decomposition is concentrated on very small neighborhoods of a small number of points.
Cite
@article{arxiv.1909.06866,
title = {Decomposition of random walk measures on the one-dimensional torus},
author = {Tom Gilat},
journal= {arXiv preprint arXiv:1909.06866},
year = {2020}
}