Séminaire groupes algébriques - Institut Élie Cartan de Lorraine

Date/heure
10 juin 2024
14:00 - 15:00

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 $μ$ . 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 $μ$ -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.