Anchored expansion and random walk
Probability
2011-11-10 v1
Abstract
This paper studies anchored expansion, a non-uniform version of the strong isoperimetric inequality. We show that every graph with i-anchored expansion contains a subgraph with isoperimetric (Cheeger) constant at least i. We prove a conjecture by Benjamini, Lyons and Schramm (1999) that in such graphs the random walk escapes with a positive lim inf speed. We also show that anchored expansion implies a heat-kernel decay bound of order exp(-c n^1/3).
Cite
@article{arxiv.math/0102199,
title = {Anchored expansion and random walk},
author = {Balint Virag},
journal= {arXiv preprint arXiv:math/0102199},
year = {2011}
}
Comments
16 pages