Random walks on Gromov hyperbolic spaes and Teichmüller spaces. Pacific Dynamics Seminar

n this talk, I will discuss random walks on Gromov hyperbolic spaces. Due
to the hyperbolicity of the spaces, random walks exhibit behaviors that
differ from the classic (Euclidean) ones. These behaviors include the
escape to infinity, central limit theorems when centered at the escape
rate, and geodesic tracking. I will explain how one can sharpen these
behaviors based on the recent observations by Gouëzel and Baik-Choi-Kim. If
time allows, I will also explain how one can implement this theory on
(non-hyperbolic) Teichmüller spaces.