Processes on Unimodular Random Networks
David J. Aldous, University of California, Berkeley
Russell Lyons, Indiana University
Abstract
We investigate unimodular random networks.
Our motivations include
their characterization via reversibility of an associated random walk
and their similarities to unimodular quasi-transitive graphs.
We extend various theorems concerning random walks, percolation, spanning
forests, and amenability from the known context of unimodular
quasi-transitive graphs to the more general context of unimodular random
networks.
We give properties of a trace associated to unimodular random networks
with applications to stochastic comparison of
continuous-time random walk.
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