Date/heure
10 juin 2024
14:00 - 15:00
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Corentin Le Bars
Catégorie d'évènement Séminaire de géométrie complexe
Résumé
Title: Random walks on affine buildings of type \tilde{A}_2.Summary:Let $G$ be a group acting on a building $X$ of type $\tilde{A}_2$ and let ${Z_n}$ 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 ${Z_n o}$, for $o$ a point 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 ${Z_n o}$. 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.