Abstract:

Let G be a group acting on a separable building X of type A2tilde and let Zn be a random walk on the group G, generated by an admissible measure mu. The purpose of the talk is to investigate some properties of the measured dynamical system Zn.o, for o a vertex of the building X. Using tools from boundary theory and the geometry of such buildings, we can prove that there exists a unique mu-stationary measure supported on the chambers of the spherical building at infinity. If time allows it, we will discuss some applications about the asymptotic properties of the random walk Zn.o. I will try to introduce most notions: (affine) buildings and their boundaries, random walks and stationary measures, the Poisson-Furstenberg boundary and some of its ergodic properties.