Anchored expansion and random walk

By B'alint Vir'ag. 2001

48 citations recorded by the source corpus.

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(—cn1/3).

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5883bdbb8afc93589ac852c3198099b400a0b899

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

A note on percolation on $Z^d$: isoperimetric profile via exponential cluster repulsion (2007, unknown): “It is easy to see that |∂+ C ( S C )|/|∂+E ( S C )| ≤ |∂C S|/|∂ES|, which implies that IP∗ψ survives.”
Probability on Trees and Networks (2017, background): “This extends Theorem 5 of Abért, Glasner, and Virág (2011). We may assume that cycles of length exactly L are traversed with positive frequency with positive probability.”
Hyperbolic and Parabolic Unimodular Random Maps (2016, result): “ by the type of (M;ˆ)? Most hyperbolic maps encountered in practice have pn(ˆ;ˆ) decaying superpolynomially (when the maps have bounded degree and anchored expansion, this follows from the results of [66]). However, for each ">0, it is possible to construct a hyperbolic unimodular random roo”
Planar stochastic hyperbolic triangulations (2016, methodology): “See [37] for background on anchored expansion.”