Title: Random walks on tori and an application to normality of numbers in self-similar sets.
Speaker: Yiftah Dayan
Speaker Info: Tel Aviv University
We show that under certain conditions, random walks on a d-dim torus by affine expanding maps have a unique stationary measure which is Haar measure. In this case, one may deduce that for every starting point in the torus, almost every trajectory of the random walk is equidistributed w.r.t. Haar measure. As an application of this result, we 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.Date: Tuesday, January 14, 2020
Joint work with Arijit Ganguly and Barak Weiss.