Open Access
2007 Processes on Unimodular Random Networks
David Aldous, Russell Lyons
Author Affiliations +
Electron. J. Probab. 12: 1454-1508 (2007). DOI: 10.1214/EJP.v12-463


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.


Download Citation

David Aldous. Russell Lyons. "Processes on Unimodular Random Networks." Electron. J. Probab. 12 1454 - 1508, 2007.


Accepted: 21 November 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1131.60003
MathSciNet: MR2354165
Digital Object Identifier: 10.1214/EJP.v12-463

Primary: 60C05
Secondary: 05C80 , 60K99

Keywords: amenability , equivalence relations , infinite graphs , percolation , quasi-transitive , Random walks , reversibility , sofic groups , Spanning forests , Stochastic comparison , Trace , transitivity , weak convergence

Vol.12 • 2007
Back to Top