Non-amenable Cayley graphs of high girth have Pc < Pu and mean-field exponents

Asaf Nachmias*, Yuval Peres

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., pc < pu. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the self-avoiding walk has positive speed.

Original languageEnglish
JournalElectronic Communications in Probability
Volume17
DOIs
StatePublished - 2012
Externally publishedYes

Keywords

  • Non-amenable graphs
  • Percolation
  • Self avoiding walk

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