This session will be devoted to the subject of hyperbolic groups acting on hyperbolic spaces and random walks. In the first part of the session Joseph Maher will introduce the notion of a random walk on a group with emphasis on hyperbolic groups. As part of that discussion he will introduce and discuss the notion of the Poisson boundary of a random walk.   In the second part of the session Sam Taylor will discuss his work on the counting problem for loxodromic elements of a hyperbolic group  acting on a hyperbolic space.  As part of that discussion he will he will introduce the idea of Patterson Sullivan measures.