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July 1998 Entropy for translation-invariant random-cluster measures
Timo Seppäläinen
Ann. Probab. 26(3): 1139-1178 (July 1998). DOI: 10.1214/aop/1022855747


We study translation-invariant random-cluster measures with techniques from large deviation theory and convex analysis. In particular, we prove a large deviation principle with rate function given by a specific entropy, and a Dobrushin-Lanford-Ruelle variational principle that characterizes translation-invariant random-cluster measures as the solutions of the variational equation for free energy. Consequences of these theorems include inequalities for edge and cluster densities of translation-invariant random-cluster measures.


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Timo Seppäläinen. "Entropy for translation-invariant random-cluster measures." Ann. Probab. 26 (3) 1139 - 1178, July 1998.


Published: July 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0935.60098
MathSciNet: MR1634417
Digital Object Identifier: 10.1214/aop/1022855747

Primary: 60K35
Secondary: 60F10 , 82B20 , 82B43

Keywords: large deviations , Random-cluster measure , Relative entropy , Variational principle

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 3 • July 1998
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