We prove, in all dimensions, that for a stationary Gibbs state with finite range or rapidly decreasing interaction, there is at most one infinite percolation cluster. This implies that the connectivity function is bounded away from 0.
Publié le : 1989-10-14
Classification:
Percolation,
Gibbs models,
uniqueness of the infinite cluster,
large deviations,
connectivity function,
60K35,
82A68,
60F10
@article{1176991161,
author = {Gandolfi, Alberto},
title = {Uniqueness of the Infinite Cluster for Stationary Gibbs States},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1403-1415},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991161}
}
Gandolfi, Alberto. Uniqueness of the Infinite Cluster for Stationary Gibbs States. Ann. Probab., Tome 17 (1989) no. 4, pp. 1403-1415. http://gdmltest.u-ga.fr/item/1176991161/