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October, 1989 Uniqueness of the Infinite Cluster for Stationary Gibbs States
Alberto Gandolfi
Ann. Probab. 17(4): 1403-1415 (October, 1989). DOI: 10.1214/aop/1176991161

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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Alberto Gandolfi. "Uniqueness of the Infinite Cluster for Stationary Gibbs States." Ann. Probab. 17 (4) 1403 - 1415, October, 1989. https://doi.org/10.1214/aop/1176991161

Information

Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0694.60096
MathSciNet: MR1048933
Digital Object Identifier: 10.1214/aop/1176991161

Subjects:
Primary: 60K35
Secondary: 60F10 , 82A68

Keywords: Connectivity function , Gibbs models , large deviations , percolation , uniqueness of the infinite cluster

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 4 • October, 1989
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