No percolation at criticality on certain groups of intermediate growth

2018/09/28 by Hermon, Jonathan, Hutchcroft, Tom · 2 citations
#FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1809.11112

Abstract

We prove that critical percolation has no infinite clusters almost surely on any unimodular quasi-transitive graph satisfying a return probability upper bound of the form p_n(v,v) ≤ exp[-Ω(n^γ)] for some γ>1/2. The result is new in the case that the graph is of intermediate volume growth.

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