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Anchored expansion and random walk

Balint Virag
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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).

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Balint Virag. 2001-02-26. Anchored expansion and random walk. https://doi.org/10.1007/pl00001663

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