We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with ℤ, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent definitions, and we study their ramifications. We also study its expected size and point out certain phase transitions.

中文翻译：

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无限生成组的渗透

我们给出了一个关于具有 ℤ 的非准等距群上的长程伯努利渗流过程的示例，其中对于参数的所有值，簇几乎肯定是有限的。这个随机图允许不同的等效定义，我们研究它们的后果。我们还研究了它的预期大小并指出了某些相变。