English

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).

Keywords

Cite

@article{arxiv.math/0102199,
  title  = {Anchored expansion and random walk},
  author = {Balint Virag},
  journal= {arXiv preprint arXiv:math/0102199},
  year   = {2011}
}

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16 pages