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2017 Indicable groups and $p_c<1$
Aran Raoufi, Ariel Yadin
Electron. Commun. Probab. 22: 1-10 (2017). DOI: 10.1214/16-ECP40

Abstract

A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of $\mathbb{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.

Citation

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Aran Raoufi. Ariel Yadin. "Indicable groups and $p_c<1$." Electron. Commun. Probab. 22 1 - 10, 2017. https://doi.org/10.1214/16-ECP40

Information

Received: 30 June 2016; Accepted: 27 December 2016; Published: 2017
First available in Project Euclid: 31 January 2017

zbMATH: 1360.82037
MathSciNet: MR3607808
Digital Object Identifier: 10.1214/16-ECP40

Subjects:
Primary: 60K35, 82B26, 82B43

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