Abstract: Random walks on groups acting on non-positively-curved spaces have been studied in depth. Various limiting behaviors of these random walks, including the positive escape rate, laws of large numbers and central limit theorems, were known under some geometric assumptions on the space and the group action. However, the actions of mapping class groups on Teichmüller spaces and curve complexes do not satisfy these assumptions, the former one being not Gromov hyperbolic and the latter one being not locally compact. Nonetheless, recent developments imply that many limiting behaviors of random walks on mapping class groups follow directly from the (partial) hyperbolicity of Teichmüller spaces and curve complexes. In this talk, I will focus on the principle behind these results and two possible applications: the regularity of the harmonic measure and the counting problem in mapping class groups. Partially joint with Hyungryul Baik and Dongryul M. Kim.

ID：871 9276 2553

Code：897719