Peter Kropholler

Random walks on Cayley Graphs of Soluble Groups: Connections with Linearity and Amenability.

We study how to use torsion-free coverings of certain soluble groups in order to complete a story about random walks on Cayley graphs that was begun by Pittet and Saloff-Coste. The results depend on a careful study of linear representations of coverings of groups and deals with an issue that certain soluble groups fail to be linear in a very specific way. There are connections with number theory, analysis and with the theory of t.d.l.c. groups.