| Résume | Résumé : Ergodic cocycles on groups are discrete random dynamical systems that generalize the classical random walk setting as their increments are not independent. In this talk, I will consider ergodic cocycles in hyperbolic spaces and exhibit some of their asymptotic properties: convergence to the boundary, positive drift... The approach involves Furstenberg's boundary theory and uses the Mackey range of the cocycle, which acts as a replacement of the Poisson-Furstenberg boundary of a random walk. I will present the context and introduce the main ideas. |
