Journal
GEOMETRIC AND FUNCTIONAL ANALYSIS
Volume 10, Issue 6, Pages 1588-1605Publisher
SPRINGER BASEL AG
DOI: 10.1007/PL00001663
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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(-cn(1/3)).
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