Indicable groups and Pc< 1

Aran Raoufi, Ariel Yadin

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of ℤ has a non-trivial percolation phase. Our main results prove this conjecture for certain groups, and in particular prove that any group with a non-trivial homomorphism into the additive group of real numbers satisfies the conjecture. We use this to reduce the conjecture to the case of hereditary just-infinite groups. The novelty here is mainly in the methods used, combining the methods of EIT and evolving sets, and using the algebraic properties of the group to apply these methods.

Original languageEnglish
Article number13
JournalElectronic Communications in Probability
Volume22
DOIs
StatePublished - 1 Jan 2017

Keywords

  • Cayley graphs
  • Percolation
  • Phase transition

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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