Séminaire Analyse-Proba (Charles Bordenave, mardi 10 décembre)

Le prochain séminaire Analyse-Proba aura lieu mardi 10 décembre à 10h30 en salle A711. Charles BORDENAVE (Institut de mathématiques de Marseille) nous parlera de "Cutoff for geodesic path and Brownian motion on hyperbolic manifolds."

Cutoff for geodesic path and Brownian motion on hyperbolic manifolds

Abstract
This is a joint work with Joffrey Mathien. For an ergodic dynamical system, the cutoff describes an abrupt transition to equilibrium. Historically introduced in seminal works by Diaconis, Shahshahani and Aldous for card shuffling and other random walks on finite groups, there are now numerous examples of Markov chains and Markov processes where the cutoff has been established. Most of the current examples are on finite spaces. In this talk, we study cutoff for classical processes – namely Brownian motion and geodesic paths – on compact hyperbolic manifolds, and we further develop a spectral strategy introduced by Lubetzky and Peres in 2016 for Ramanujan graphs and further developed in different geometric contexts. In particular, we extend results obtained by Golubev and Kamber in 2019 on hyperbolic surfaces to any dimension and still are able to obtain cutoff under weaker hypothesis and broader settings.