Alessandro Sisto: A central limit theorem for acylindrically hyperbolic groups

Acylindrically hyperbolic groups form a very large class of groups that includes non-elementary (relatively) hyperbolic groups, mapping class groups, Out(F_n), many groups acting on CAT(0) spaces, small cancellation groups, etc. I will discuss the behaviour of random walks on such groups, and in particular the fact, encoded by the "deviation inequalities", that random paths tend to stay close to geodesics in Cayley graphs. I will then present a few consequences of the deviation inequalities, most notably a central limit theorem for the distance from the identity of the random walk. Joint with Pierre Mathieu.