Random Walks on Products of Hyperbolic Groups

Abstract

The subject area of this thesis is the theory of random walks on groups. First, we study random walks on products of hyperbolic groups and show that the Poisson boundary can be identified with an appropriate geometric boundary (the skeleton). Second, we show that in the particular case of free and free-product factors, the Hausdorff dimension of the conditional measures on product fibers of the Poisson boundary is related to the asymptotic entropy and the rate of escape of the corresponding conditional random walks via a generalized entropy-dimension formula.