Processes on Unimodular Random Networks

David J. Aldous (University of California, Berkeley)
Russell Lyons (Indiana University)


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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Pages: 1454-1508

Publication Date: November 21, 2007

DOI: 10.1214/EJP.v12-463


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