Russ Thompson

Ph.D. (2011) Cornell University

First Position

Postdoctoral fellow at the Mathematical Sciences Research Institute

Dissertation

Random Walks and Subgroup Geometry

Advisor:

Laurent Saloff-Coste

Research Area:

probability and geometry on groups

Abstract: We study how certain properties of random walks on groups are related to the geometry of certain subgroups. In particular, we show that exponential distortion or an analog thereof implies that a random walk moves diffusively on polycyclic and some metabelian groups. In polycyclic groups we show this is invariant under choice of generating set. We also classify Erschler's critical constant for recurrence on groups of polynomial volume growth and provide a partial result for polycyclic groups. This constant gauges how spread out a measure on a group can be while leaving a particular subgroup recurrent.