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Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs
Journal of the American Mathematical Society ( IF 3.5 ) 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

中文翻译:

非单模传递图上渗透的非唯一性和平均场临界性

我们研究了非单模准传递图上的伯努利键渗透,更一般地,自同构群具有非单模准传递子群的图。我们证明在任何这样的图上的渗透都有一个非空阶段,其中有无限个光团,这意味着存在一个非空阶段,其中有无限多的无限个团。也就是说,我们证明 $p_c
更新日期:2020-09-23
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