The Annals of Probability

Entropy for translation-invariant random-cluster measures

Timo Seppäläinen

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 26, Number 3 (1998), 1139-1178.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855747

Digital Object Identifier
doi:10.1214/aop/1022855747

Mathematical Reviews number (MathSciNet)
MR1634417

Zentralblatt MATH identifier
0935.60098

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F10: Large deviations 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82B43: Percolation [See also 60K35]

Keywords
Relative entropy variational principle large deviations random-cluster measure

Citation

Seppäläinen, Timo. Entropy for translation-invariant random-cluster measures. Ann. Probab. 26 (1998), no. 3, 1139--1178. doi:10.1214/aop/1022855747. https://projecteuclid.org/euclid.aop/1022855747


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References

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  • AMES, IOWA 50011 E-MAIL: seppalai@iastate.edu