Processes on Unimodular Random Networks
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.
Cite
@article{arxiv.math/0603062,
title = {Processes on Unimodular Random Networks},
author = {David Aldous and Russell Lyons},
journal= {arXiv preprint arXiv:math/0603062},
year = {2020}
}
Comments
66 pages; 3rd version corrects formula (4.4) -- the published version is incorrect --, as well as a minor error in the proof of Proposition 4.10; 4th version corrects proof of Proposition 7.1; 5th version corrects proof of Theorem 5.1; 6th version makes a few more minor corrections