On non-uniqueness of percolation on nonamenable Cayley graphs *

@inproceedings{Pak2000OnNO,
  title={On non-uniqueness of percolation on nonamenable Cayley graphs *},
  author={Igor Pak and Tatiana SMIRNOVA-NAGNIBEDA},
  year={2000}
}
  • Igor Pak, Tatiana SMIRNOVA-NAGNIBEDA
  • Published 2000
The aim of this Note is to prove a weak version of the conjecture of Benjamini and Schramm about phase of non-uniqueness for the Bernoulli bond percolation on nonamenable transitive graphs. We show that every nonamenable finitely generated group has a finite system of generators such that the Bernoulli bond percolation on the corresponding Cayley graph has a nonempty non-uniqueness phase. Together with previously known results, this gives a characterization of amenability of finitely generated… CONTINUE READING
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