Counterexamples for percolation on unimodular random graphs
Counterexamples for percolation on unimodular random graphs
We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with p c = p u for Bernoulli bond percolation, as well as an example of a bounded degree, unimodular random rooted graph with p c < 1 but with an infinite cluster at criticality.These examples show …