Site recurrence for coalescing random walk
Probability
2015-10-19 v1
Abstract
Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.
Cite
@article{arxiv.1510.04721,
title = {Site recurrence for coalescing random walk},
author = {Itai Benjamini and Eric Foxall and Ori Gurel-Gurevich and Matthew Junge and Harry Kesten},
journal= {arXiv preprint arXiv:1510.04721},
year = {2015}
}
Comments
11 pages