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2012 Non-amenable Cayley graphs of high girth have $p_c < p_u$ and mean-field exponents
Asaf Nachmias, Yuval Peres
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Electron. Commun. Probab. 17(none): 1-8 (2012). DOI: 10.1214/ECP.v17-2139

Abstract

In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., $p_c< p_u$. 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.

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Asaf Nachmias. Yuval Peres. "Non-amenable Cayley graphs of high girth have $p_c < p_u$ and mean-field exponents." Electron. Commun. Probab. 17 1 - 8, 2012. https://doi.org/10.1214/ECP.v17-2139

Information

Accepted: 3 December 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1302.82056
MathSciNet: MR3005730
Digital Object Identifier: 10.1214/ECP.v17-2139

Subjects:
Primary: 82B43

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