Random walks on (hyperbolic) groups

the first part of the talk will be an introduction to the general
theory of random walks on groups with some classical results on entropy,
rate of escape ... . For hyperbolic groups, these probabilistic objects
have geometric counterparts in terms of Gromov boundary, quasi-conformal
measures ... I will mention applications and open questions.
Finally I will discuss fluctuation results - like the central limit
theorem - in particular a recent work with A. Sisto on deviation
inequalities for random walks on cylindrically hyperbolic groups.