Speaker: Debanjan Nandi, IISc
November 29, 2024 02:30 PM
- 03:30 PM
Abstract:
We will discuss potential theoretic properties of a Markov process which allow a Lyons-Sullivan type discretization of the process to suitable discrete subsets of Gromov hyperbolic spaces, so that the discretized Markov process captures to a large extent the potential theoretic properties of the original process. Orbits of a large class of groups acting properly discontinuously by isometries appear as Important examples of such subsets, the discretized process in this case being a random walk in the group. This includes for example the class of groups acting geometrically finitely. The Martin boundary of the random walk is identified with the limit set of the action. In specific cases, for example for groups with finite volume quotients, the random walk has finite exponential moment with respect to a geometric norm. The talk will be based on joint work with Werner Ballmann and Panagiotis Polymerakis.