Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

The triangle and the open triangle

Gady Kozma

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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”.

Article information

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

First available in Project Euclid: 4 January 2011

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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

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


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.

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