Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

The triangle and the open triangle

Gady Kozma

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Abstract

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

Résumé

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

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 1 (2011), 75-79.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1294170230

Digital Object Identifier
doi:10.1214/09-AIHP352

Mathematical Reviews number (MathSciNet)
MR2779397

Zentralblatt MATH identifier
1221.60140

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35] 20P05: Probabilistic methods in group theory [See also 60Bxx] 47N30: Applications in probability theory and statistics

Keywords
Percolation Cayley graph Mean-field Triangle condition Operator theory Spectral theory

Citation

Kozma, Gady. The triangle and the open triangle. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 1, 75--79. doi:10.1214/09-AIHP352. https://projecteuclid.org/euclid.aihp/1294170230


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