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Is the critical percolation probability local? (English) Zbl 1230.60099
Authors’ abstract: “We show that the critical probability for percolation on a \(d\)-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite \(d\)-regular tree. We also prove a finite analogue of this statement, valid for expander graphs, without any girth assumption.”

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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