Two Badly Behaved Percolation Processes on a Nonunimodular Graph

Olle Häggström ()
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Olle Häggström: Chalmers University of Technology

Journal of Theoretical Probability, 2013, vol. 26, issue 4, 1165-1180

Abstract: 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 ∞. The second property is that speed of random walk on an infinite cluster is almost surely well defined.

Keywords: Percolation; Random walk; Encounter points; Unimodularity; Mass transport; 60K35 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0397-9

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