Coalescing random walk on unimodular graphs
Probability
2018-04-06 v3
Abstract
Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected lifetime. Additionally, we deduce an adaptation of our main theorem that holds uniformly for coalescing random walk on finite random unimodular graphs with degree distribution stochastically dominated by a probability measure with finite mean.
Cite
@article{arxiv.1701.02653,
title = {Coalescing random walk on unimodular graphs},
author = {Eric Foxall and Tom Hutchcroft and Matthew Junge},
journal= {arXiv preprint arXiv:1701.02653},
year = {2018}
}
Comments
Corrected an error in the previous argument and added two new corollaries