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September 2011 Percolation on a product of two trees
Gady Kozma
Ann. Probab. 39(5): 1864-1895 (September 2011). DOI: 10.1214/10-AOP618

Abstract

We show that critical percolation on a product of two regular trees of degree ≥ 3 satisfies the triangle condition. The proof does not examine the degrees of vertices and is not “perturbative” in any sense. It relies on an unpublished lemma of Oded Schramm.

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Gady Kozma. "Percolation on a product of two trees." Ann. Probab. 39 (5) 1864 - 1895, September 2011. https://doi.org/10.1214/10-AOP618

Information

Published: September 2011
First available in Project Euclid: 18 October 2011

zbMATH: 1243.60078
MathSciNet: MR2884876
Digital Object Identifier: 10.1214/10-AOP618

Subjects:
Primary: 60K35
Secondary: 60B99

Keywords: mean-field , Nonamenable groups , Percolation on groups , product of trees , Triangle condition

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 5 • September 2011
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