Random walk on the infinite cluster of the percolation model
type: Item
instance of: scholarly article
title: Random walk on the infinite cluster of the percolation model
zbMATH Open document ID: 0791.60095
DOI: 10.1007/BF01195881
author: G. R. Grimmett
author: Harry Kesten
author: Y. Zhang
publication date: 1994-07-14T00:00:00Z
review text: We consider random walk on the infinite cluster of bond percolation on \(\mathbb{Z}^ d\). We show that, in the supercritical regime when \(d \geq 3\), this random walk is a.s. transient. This conclusion is achieved by considering the infinite percolation cluster as a random electrical network in which each open edge has unit resistance. It is proved that the effective resistance of this network between a nominated point and the points at infinity is almost surely finite.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 82B43
Mathematics Subject Classification ID: 82D30
zbMATH DE Number: 569066
zbMATH Keywords: random walk
zbMATH Keywords: infinite cluster
zbMATH Keywords: bond percolation
zbMATH Keywords: infinite percolation cluster as a random electrical network
zbMATH Keywords: effective resistance
MaRDI profile type: Publication
cites work: An invariance principle for reversible Markov processes. Applications to random motions in random environments
cites work: Q4693063
cites work: The supercritical phase of percolation is well behaved
cites work: Q3814484
cites work: Q3672870
cites work: The probability of a large cluster in supercritical Bernoulli perlocation
cites work: A simple criterion for transience of a reversible Markov chain
cites work: Q3281447
cites work: Effective conductivity of homogeneous random sets
full work available at URL: https://doi.org/10.1007/bf01195881
OpenAlex ID: W1964366669
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569066