منابع مشابه
Anchored expansion and random walk
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 im...
متن کاملAnchored Expansion and Random Walk
This paper studies anchored expansion, a non-uniform version of the strong isoperi-metric 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 (1998) that in such graphs the random walk escapes with a positive lim inf speed. We also show that anchored expansion i...
متن کاملThe Speed of Simple Random Walk and Anchored Expansion on Percolation Clusters: an Overview
Benjamini, Lyons and Schramm (1999) considered properties of an infinite graph G, and the simple random walk on it, that are preserved by random perturbations. To address problems raised by those authors, we study simple random walk on the infinite percolation cluster in Cayley graphs of certain amenable groups known as “lamplighter groups”. We prove that zero speed for random walk on a lamplig...
متن کاملA Random Walk with Exponential Travel Times
Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...
متن کاملAnchored expansion, percolation and speed
Benjamini, Lyons and Schramm [Random Walks and Discrete Potential Theory (1999) 56–84] considered properties of an infinite graph G, and the simple random walk on it, that are preserved by random perturbations. In this paper we solve several problems raised by those authors. The anchored expansion constant is a variant of the Cheeger constant; its positivity implies positive lower speed for the...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2000
ISSN: 1016-443X
DOI: 10.1007/pl00001663