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Entropy for Translation-Invariant Random-Cluster Measures

Timo Seppalainen
The Annals of Probability
Vol. 26, No. 3 (Jul., 1998), pp. 1139-1178
Stable URL: http://www.jstor.org/stable/2652742
Page Count: 40
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Entropy for Translation-Invariant Random-Cluster Measures
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Abstract

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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