Regularity of the drift and entropy of random walks on groups

Abstract

Random walks on a group $G$ model many natural phenomena. A random walk is defined by a probability measure $p$ on $G$. We are interested in asymptotic properties of the random walks and in particular in the linear drift and the asymptotic entropy. If the geometry of the group is rich, then these numbers are both positive and the way of dependence on $p$ is itself a property of $G$. In this note, we review recent results about the regularity of the drift and the entropy for free groups, free products and hyperbolic groups.

13 pages

References in corpus (1)

• Asymptotic entropy and green speed for random walks on countable groups

Cited by in corpus (1)

• Dimension of harmonic measures in hyperbolic spaces