Entropy for translation-invariant random-cluster measures

• 成果类型: Article
• 署名作者: Seppalainen, T
• 署名单位: Iowa State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1139-1178
• 关键词: large deviations; sure quasilocality; percolation models; lattice systems; potts-model; uniqueness; REPRESENTATION; FIELDS; graph; TREE

摘要

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.