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
Uniqueness of the infinite cluster for stationary Gibbs states / A. Gandolfi. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - STAMPA. - 17:(1989), pp. 1403-1415. [10.1214/aop/1176991161]
Uniqueness of the infinite cluster for stationary Gibbs states
GANDOLFI, ALBERTO
1989
Abstract
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
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