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Seppäläinen, Timo

Entropy for translation-invariant random-cluster measures. (English) Zbl 0935.60098

Ann. Probab. 26, No. 3, 1139-1178 (1998).
Summary: 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.

Cited in 5 Documents

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F10 Large deviations
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B43 Percolation

Keywords:

relative entropy; variational principle; large deviations; random-cluster measure
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\textit{T. Seppäläinen}, Ann. Probab. 26, No. 3, 1139--1178 (1998; Zbl 0935.60098)
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References:

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