The classical random walk on an integer lattice Z^d is often (aptly) described by the colloquial catch-phrase: "A drunken man always finds his way home, but a drunken bird may get lost forever". I will discuss the case for random walks on word hyperbolic groups. The goal will be to understand the connection between the (analytic) exit measure for a large class of 'nice' random walks on the group and the (geometric) Patterson-Sullivan measure on the boundary of the group. This is based on a result of Gouëzel-Mathéus-Maucourant. No background on random walks will be assumed. Speaker(s): Mitul Islam (UM)