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Processes on Unimodular Random Networks

David Aldous·Russell Lyons
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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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David Aldous, Russell Lyons. 2006-03-02. Processes on Unimodular Random Networks. https://arxiv.org/abs/math/0603062

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