Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs,Journal of the American Mathematical Society

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Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs
Journal of the American Mathematical Society ( IF 3.9 ) Pub Date : 2020-09-23 , DOI: 10.1090/jams/953
Tom Hutchcroft

We study Bernoulli bond percolation on nonunimodular quasi-transitive graphs, and more generally graphs whose automorphism group has a nonunimodular quasi-transitive subgroup. We prove that percolation on any such graph has a non-empty phase in which there are infinite light clusters, which implies the existence of a non-empty phase in which there are infinitely many infinite clusters. That is, we show that $p_c

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