Published online by Cambridge University Press: 20 February 2020
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.
Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 639046).