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Processes on unimodular random networks. (English) Zbl 1131.60003

Electron. J. Probab. 12, 1454-1508 (2007); errata ibid. 22, Paper No. 51, 4 p. (2017); ibid. 24, Paper No. 25, 2 p. (2019).
Summary: 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.

MSC:

60C05 Combinatorial probability
60K99 Special processes
05C80 Random graphs (graph-theoretic aspects)
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