Dynamics Seminar

Event Information Random walks in hyperbolic spaces
15:10 on Wednesday September 14, 2016
16:00 on Wednesday September 14, 2016
BA6180, Bahen Center, 40 St. George St.
Giulio Tiozzo

University of Toronto

We will consider random walks on spaces of isometries of hyperbolic spaces, trying to understand their asymptotic properties. If the space has negative curvature, then it has a non-trivial topological boundary. We will be interested in comparing the boundary theory of the random walk with the topological notion.

1) Boundary convergence: We will prove the theorem of Furstenberg which states that a random walk on SL_2(R) converges to the boundary of the hyperbolic plane almost surely.

2) The Poisson-Furstenberg boundary: We will discuss how to attach a general notion of boundary to any random walk on a group, and what are the criteria which allow one to identify this general measurable boundary with a topological boundary which is given by the geometry.