Abstract
Considering G as a countable infinite group and μ a symmetric probability on it whose support generates G, and calling μ a generating measure of G. Here, we prove that for some probability μ, group G admits a long-range percolation phase transition in which the corresponding percolation threshold λc(μ) is finite. Consequently, the group invariant λc(G)=infμλc(μ) is well-defined, where the infimum is taken over all generating measures μ.
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