Geometry MMA Seminar: Entropy and drift for random walks on cocompact Fuchsian groups

Speaker: Giulio Tiozzo, University of Toronto

Title:   Entropy and drift for random walks on cocompact Fuchsian groups

Abstract:  A recurring question in the theory of random walks on groups of isometries of hyperbolic spaces asks whether the hitting measures can coincide with measures of geometric origin, such as the Lebesgue measure. This is also related to the inequality between entropy and drift.

We will prove that the inequality between entropy and drift is strict for certain random walks on cocompact Fuchsian groups.
As a consequence, the dimension of the hitting measure is strictly less than one.  As we will see, this is also related to a geometric inequality for geodesic lengths, strongly reminiscent of the Anderson-Canary-Culler-Shalen inequality for free Kleinian groups.

Joint w. Petr Kosenko.
 

Time: Monday, September 26, 2022 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208