Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Random walks on tori and an application to normality of numbers in self-similar sets

Talk by Yiftach Dayan

**Date:** 29.03.21 **Time:** 15.00 - 16.15 **Room:** ETH HG G 19.2

We show that under certain conditions, random walks on a d-dim torus by affine expanding maps have a unique stationary measure. We then use this result to show that given an IFS of contracting similarity maps of the real line with a uniform contraction ratio 1/D, where D is some integer > 1, under some suitable condition, almost every point in the attractor of the given IFS (w.r.t. a natural measure) is normal to base D. (Joint work with Arijit Ganguly and Barak Weiss.)