The central limit theorem of random walks answers the question "how quickly does the random walk drift away from the origin". Historically, it has been proven (under some assumptions) for free groups, hyperbolic groups, and various generalizations of hyperbolic groups. We proved this for one generalization of hyperbolic groups: groups containing superlinear divergent quasi-geodesics. The advantage of this setting compared to previous versions of CLT is that it is invariant under quasi-isometry.
In this talk, I will delve into the superlinear divergence property, as well as its geometric consequences that led to the theory of random walks on groups containing superlinear divergent quasi-geodesics. This talk is based on joint work with Kunal Chawla, Inhyeok Choi, and Kasra Rafi.