Random walks on groups and superlinear divergent geodesics

Kunal Chawla (Princeton)

Abstract: A theme in the study of random walks on groups is that "negative curvature" implies strong quantitative control on behaviour of random walks. Over the past twenty years, various researchers have established manifestations of this principle - proving limit laws for random walks on trees, hyperbolic groups, and groups acting on hyperbolic spaces. At the same time, many forms of "negative curvature" are expected or known to be quasi-isometry invariant. We investigate random walks on groups with superlinear divergent geodesics, and use new techniques to establish a quasi-isometry invariant criterion for a group to satisfy a central limit theorem. This is joint work with Inhyeok Choi, Vivian He, and Kasra Rafi.