On non-uniqueness of percolation on non-amenable Cayley graphs
by Inessa Epstein
Abstract: We show that every non-amenable finitely generated group admits
a system of generators such that the Bernoulli edge percolation on the
corresponding Cayley graph has a non-empty non-uniqueness phase. We also
discuss an application to measure preserving ergodic actions by
non-amenable countable groups on standard Borel spaces.
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