| Processes on Unimodular Random Networks (2006) | |||||||||
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.. Comment: 66 pages; last version corrects formula (4.4) -- the published version is incorrect --, as well as a minor error in the proof of Proposition 4.10 | |||||||||
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