Anchored expansion and random walk

Details Anchored expansion and random walk Anchored expansion and random walk

2001-02-26

arxiv.org/abs/math/0102199v1

Geom. Funct. Anal. 10 (2000), no. 6, 1588-1605

Mathematics

Probability

16 pages

Scientific paper

10.1007/PL00001663

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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