Two Badly Behaved Percolation Processes on a Nonunimodular Graph |
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| Authors: | Olle Häggström |
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| Institution: | 1. Dept. of Mathematical Sciences, Chalmers University of Technology, 412 96, Goteborg, Sweden
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| 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. |
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