LA Probability Forum

USC KAP 414

In this talk the speaker will present a method which can be used to establish a formula which relates the Hausdorff dimension of the harmonic measure with the entropy and drift for non-degenerate finitely supported random walks on $\mathbb{Z}/2\mathbb{Z} \wr \mathbb{Z}$, following the approach of R. Tanaka for hyperbolic-like groups. The speaker will also relate our approach to recently announced results due to Josh Frisch and Eduardo Silva. If time permits, the speaker will discuss how we can use our techniques to establish the continuity of the asymptotic drift and the Hausdorff dimension with respect to the choice of the step distribution, and whether our results can be generalized to random walks on lamplighters on trees and hyperbolic groups. Joint work (in progress) with Eduardo Silva.