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February 2011 The triangle and the open triangle
Gady Kozma
Ann. Inst. H. Poincaré Probab. Statist. 47(1): 75-79 (February 2011). DOI: 10.1214/09-AIHP352

Abstract

We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.

Nous montrons que dans le cas de la percolation sur un graphe transitif la “condition du triangle” est équivalente à celle du “triangle ouvert”.

Citation

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Gady Kozma. "The triangle and the open triangle." Ann. Inst. H. Poincaré Probab. Statist. 47 (1) 75 - 79, February 2011. https://doi.org/10.1214/09-AIHP352

Information

Published: February 2011
First available in Project Euclid: 4 January 2011

zbMATH: 1221.60140
MathSciNet: MR2779397
Digital Object Identifier: 10.1214/09-AIHP352

Subjects:
Primary: 20P05 , 47N30 , 60K35 , 82B43

Keywords: Cayley graph , mean-field , operator theory , percolation , Spectral theory , Triangle condition

Rights: Copyright © 2011 Institut Henri Poincaré

Vol.47 • No. 1 • February 2011
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