Two Badly Behaved Percolation Processes on a Nonunimodular Graph
Journal article, 2013
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.
infinite clusters
trees
Random walk
Unimodularity
Encounter points
Percolation
invariant percolation
uniqueness
spanning forests
Mass
transport
Author
Olle Häggström
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Journal of Theoretical Probability
0894-9840 (ISSN) 1572-9230 (eISSN)
Vol. 26 4 1165-1180Subject Categories
Mathematics
DOI
10.1007/s10959-011-0397-9