David Revelle

Ph.D. (2002) Cornell University

First Position

NSF postdoctoral position at the University of California at Berkeley Department of Statistics

Dissertation

Random Walks on Solvable Groups

Advisor:

Laurent Saloff-Coste

Research Area:

Random Walks on Groups

Abstract: We study a number of questions about random walks on solvable groups. For random walks on nilpotent groups, we determine which subgroups are recurrent, and for a random walk on the Heisenberg group, we study the number of distinct visited cosets at time n.

The bulk of the examples considered are about the behavior of random walks away from their starting point in groups of exponential growth. In particular, we examine the rate of escape of some inward biased random walks, as well as some unbiased walks that have an intermediate escape rate. We also compute asymptotics for transition probabilities on some semi-direct products, both at the origin and at more general points.