Geodesics and recurrence of random walks in disordered systems
type: Item
instance of: scholarly article
title: Geodesics and recurrence of random walks in disordered systems
zbMATH Open document ID: 1013.60072
author: Daniel Boivin
author: Jean-Marc Derrien
published in: Electronic Communications in Probability
publication date: 2003-02-25T00:00:00Z
full work available at URL: https://eudml.org/doc/122684
full work available at URL: paper11.abs.html
review text: There are two parts, both concerned with random environment on the edges of \(\mathbb Z^d\). Criteria, especially the order of moment conditions, are precised and/or illustrated through many counter-examples. The first part is about the number of geodesics in first-passage percolation model in \(\mathbb Z^2\). The result of \textit{J. Wehr} [J. Stat. Phys. 87, No. 1-2, 439-447 (1997; Zbl 0937.82020)] for this number to be either \(0\) or \(+\infty\) is improved. A counter-example is constructed where a unique geodesic filling the space is prescribed. The second part is about transience/recurrence criteria for the associated reversible random walk, referring to results of Peres in [\textit{N. Berger}, Commun. Math. Phys. 226, No. 3, 531-558 (2002; Zbl 0991.82017)]. The transience criterion in \(\mathbb Z^d\), \(d \geq 3\), is improved.
reviewed by: Thierry Delmotte
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K37
zbMATH DE Number: 1873762
zbMATH Keywords: random environment
zbMATH Keywords: geodesics
zbMATH Keywords: random walks
MaRDI profile type: Publication
DOI: 10.1214/ECP.V7-1052
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description: scientific article; zbMATH DE number 1873762