English

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 SS of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one μ1\mu_1 has the property that the random walk with initial distribution μ1\mu_1 evolved by the action of SS equidistributes very fast. The second measure μ2\mu_2 in the decomposition is concentrated on very small neighborhoods of a small number of points.

Keywords

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}
}