Electronic Journal of Probability

Processes on Unimodular Random Networks

David Aldous and Russell Lyons

Full-text: Open access

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.

Article information

Source
Electron. J. Probab. Volume 12 (2007), paper no. 54, 1454-1508.

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

Permanent link to this document
http://projecteuclid.org/euclid.ejp/1464818525

Digital Object Identifier
doi:10.1214/EJP.v12-463

Mathematical Reviews number (MathSciNet)
MR2354165

Zentralblatt MATH identifier
1131.60003

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 60K99: None of the above, but in this section 05C80: Random graphs [See also 60B20]

Keywords
Amenability equivalence relations infinite graphs percolation quasi-transitive random walks transitivity weak convergence reversibility trace stochastic comparison spanning forests sofic groups

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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. http://projecteuclid.org/euclid.ejp/1464818525.


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