Brownian motion and geodesic flow in pinched negative curvature

schedule le mardi 30 novembre 2021 de 10h30 à 12h00

Organisé par : David Burguet, Yves Coudene et Pierre-Antoine Guiheneuf

Intervenant : Jaelin Kim (LPSM)
Lieu : salle 16.26.209

Sujet : Brownian motion and geodesic flow in pinched negative curvature

Résumé :


In negatively curved Cartan-Hadamard manifolds, the Brownian distance has linear growth and the log of Green’s function along Brownian paths has linear decay with probability 1. In this talk, I will prove the central limit theorem for these random variables in negatively curved C-H manifolds with a non-uniform lattice. The Brownian motion gives rise to a Gibbs measure. I provide the ergodic properties of this Gibbs measure. I will conclude with a description of dynamical and probabilistic aspects of asymptotic harmonicity.