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

### Tom Gilat (Bar-Ilan University)

*Thursday, January 23, 2020,
11:10 – 12:00*,
**-101**

**Abstract:**

The main result in this talk 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.