Title:“Large deviations for random walks without moment conditions on hyperbolic spaces”.

Abstract: Consider a random walk on a hyperbolic space (the talk will mostly focuss on the special case of trees). It is known that the walk is converging almost surely towards a point at a boundary, and that the rate of escape is positive. We will discuss quantitative versions of these statements: when can one show that these facts hold with an exponentially small probability for exceptions? While there are several such results in the literature, the originality of our approach is that it does not require any moment condition on the random walk. We will discuss the main technical new idea in the case of the free group.