Is the critical percolation probability local?

Itai Benjamini, Asaf Nachmias, Yuval Peres

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)261-269
Number of pages9
JournalProbability Theory and Related Fields
Volume149
Issue number1
DOIs
StatePublished - Mar 2011
Externally publishedYes

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