# Random walks on hyperbolic groups

**Note that the talk on 27th of May is scheduled for 13:15-14:45.****Note that the talk on 6th of June is scheduled for 10:30-12:00.**

The aim of the course is to discuss the interplay between the geometry of a group and the behavior of random walk paths in the group. We shall be concerned with non-amenable hyperbolic or acylindrically hyperbolic groups e.g. fundamental groups of surfaces and Mapping Class groups. The main results we can prove are about fluctuations of random paths: estimate for the variance of the distance to the initial point, central limit theorems, regularity of the rate of escape in terms of the driving measure. Our main tool are so-called 'deviation inequalities', as defined in [Mathieu-Sisto, Deviation inequalities and CLT for random walks on acylindrically hyperbolic groups, Preprint 2015. Available on Arxiv.] On the way, we shall recall basic notions about random walks on groups: entropy, Poisson boundaries…