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 λ c ( μ ) is finite. Consequently, the group invariant λ c ( G ) = inf μ λ c ( μ ) is well-defined, where the infimum is taken over all generating measures μ .

中文翻译：

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每一个可数的无限群都允许一个相变的长距离渗透

摘要 将 G 视为可数无穷群，μ 是其支持生成 G 的对称概率，称 μ 为 G 的生成测度。在这里，我们证明对于某个概率 μ，G 组允许长程渗流相变，其中相应的渗流阈值 λ c ( μ ) 是有限的。因此，群不变量 λ c ( G ) = inf μ λ c ( μ ) 是明确定义的，其中对所有生成度量 μ 都采用了下限。