Electronic Journal of Probability
- Electron. J. Probab.
- Volume 12 (2007), paper no. 54, 1454-1508.
Processes on Unimodular Random Networks
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.
Electron. J. Probab., Volume 12 (2007), paper no. 54, 1454-1508.
Accepted: 21 November 2007
First available in Project Euclid: 1 June 2016
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Zentralblatt MATH identifier
Amenability equivalence relations infinite graphs percolation quasi-transitive random walks transitivity weak convergence reversibility trace stochastic comparison spanning forests sofic groups
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Aldous, David; Lyons, Russell. Processes on Unimodular Random Networks. Electron. J. Probab. 12 (2007), paper no. 54, 1454--1508. doi:10.1214/EJP.v12-463. https://projecteuclid.org/euclid.ejp/1464818525