Timothée Bénard, University of Cambridge

Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following inverse problem: how much information on the law of increment of the walk can be deduced from the harmonic measure at infinity? I will explain how one can address this question by studying some winding statistics of a typical geodesic ray on the group chosen randomly by the harmonic measure.