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

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”.

DOI : https://doi.org/10.1214/09-AIHP352
Classification:  60K35,  82B43,  20P05,  47N30
Keywords: percolation, Cayley graph, mean-field, triangle condition, operator theory, spectral theory
@article{AIHPB_2011__47_1_75_0,
     author = {Kozma, Gady},
     title = {The triangle and the open triangle},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {1},
     year = {2011},
     pages = {75-79},
     doi = {10.1214/09-AIHP352},
     zbl = {1221.60140},
     mrnumber = {2779397},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_1_75_0}
}
Kozma, Gady. The triangle and the open triangle. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 1, pp. 75-79. doi : 10.1214/09-AIHP352. http://www.numdam.org/item/AIHPB_2011__47_1_75_0/

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