Continuity of Asymptotic Characteristics for Random Walks on Hyperbolic Groups

We describe a new approach to proving the continuity of asymptotic entropy as a function of a transition measure under a finite first moment condition. It is based on using conditional random walks and amounts to checking uniformity in the strip criterion for the identification of the Poisson boundary. It is applicable to word hyperbolic groups and in several other situations when the Poisson boundary can be identified with an appropriate geometric boundary.