Random walks, superlinear divergence and quasi-isometry
Since Bellman, Furstenberg and Kesten’s pioneering works, random walks on groups have been investigated from the viewpoint of dynamics, ergodic theory and geometric group theory. A long-sought goal in this direction is to relate a group’s QI-invariant property with the limiting behaviour of random walks on that group. Recently, Goldsborough and Sisto formulated a certain QI-invariant property of a group, with both an intrinsic and an extrinsic flavor, that leads to CLT of random walks on that group. In this talk, I will explain this CLT from the intrinsic point of view. Joint with Kunal Chawla, Vivian He and Kasra Rafi.