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Two Badly Behaved Percolation Processes on a Nonunimodular Graph

Journal article
Authors Olle Häggström
Published in Journal of Theoretical Probability
Volume 26
Issue 4
Pages 1165-1180
ISSN 0894-9840
Publication year 2013
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 1165-1180
Language en
Links dx.doi.org/10.1007/s10959-011-0397-...
Keywords Percolation, Random walk, Encounter points, Unimodularity, Mass, transport, invariant percolation, infinite clusters, spanning forests, uniqueness, trees
Subject categories Mathematics

Abstract

We provide nonunimodular counterexamples to two properties that are well known for automorphism invariant percolation on unimodular transitive graphs. The first property is that the number of encounter points in an infinite cluster is almost surely 0 or a. The second property is that speed of random walk on an infinite cluster is almost surely well defined.

Page Manager: Webmaster|Last update: 9/11/2012
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