Random walks on affine buildings of type \tilde{A}_2.
Corentin Le Bars (Weizmann Institute of Science)
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathe/veranstaltungen/wissenschaftliche_veranstaltungen/oberseminar_algebra_geometrie_topologie/termine/lebars
- Random walks on affine buildings of type \tilde{A}_2.
- 2024-11-12T16:00:00+01:00
- 2024-11-12T18:00:00+01:00
- Corentin Le Bars (Weizmann Institute of Science)
12.11.2024 von 16:00 bis 18:00 (Europe/Berlin / UTC100)
Hörsaal 111
Summary: Let $G$ be a group acting on a possibly non-discrete 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 Furstenberg's 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. This is the first step in a more advanced study of the random walk, but this result can also be used in other contexts. I will discuss some of these applications, among which some asymptotic properties of the random walk, and some structural results on the acting group (Tits alternative). 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.