Apparaît dans la collection : 2022 - T2 - WS3 - Hyperbolic groups and their generalisations

Let G be a group acting on a Cat(0) cubical complex X. Consider a random walk Z_n=g_1...g_n on G, obtained by multiplying independently chosen random elements g_i of the same law. If x_0 is an origin in X, we prove that the random variable d(Z_nx_0,x_0) satisfies a Central Limit Theorem. Along the way, we obtain a nice characterization of the boundary of the contact graph of X, as a subset of the Roller boundary. This is a joint work with Talia Fernós and Frédéric Mathéus.