Volume growth and random walks on graphs

Matthew Folz
Tue, Jun 5, 2012
PIMS, University of British Columbia
PIMS-MPrime Summer School in Probability
We discuss various behaviours of continuous time simple random walks which are governed by the volume growth of the underlying weighted graph. In this setting the volume growth is computed with respect to a metric adapted to the random walk and not the graph metric. Use of these metrics allows us to establish results for graphs which are analogous to those for diffusions on a manifold or the Markov process associated with a strongly local Dirichlet form.