The triangle and the open triangle
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 1, pp. 75-79.

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

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

DOI : 10.1214/09-AIHP352
Classification : 60K35, 82B43, 20P05, 47N30
Mots-clés : percolation, Cayley graph, mean-field, triangle condition, operator theory, spectral theory 
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Kozma, Gady. The triangle and the open triangle. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 1, pp. 75-79. doi : 10.1214/09-AIHP352. http://www.numdam.org/articles/10.1214/09-AIHP352/

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