Processes on Unimodular Random Networks

Details Processes on Unimodular Random Networks Processes on Unimodular Random Networks

2006-03-02

arxiv.org/abs/math/0603062v4

Electron. J. Probab. 12, Paper 54 (2007), 1454-1508

Mathematics

Probability

66 pages; 3rd version corrects formula (4.4) -- the published version is incorrect --, as well as a minor error in the proof o

Scientific paper

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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