BK-type inequalities and generalized random-cluster representations

DOI10.1007/s00440-012-0452-1zbMath1279.60125arXiv1203.3665OpenAlexW2170321617MaRDI QIDQ377509

Alberto Gandolfi, Jacob Van Den Berg

Publication date: 6 November 2013

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3665

zbMATH Keywords

Gibbs distributionBK inequalitynegative dependenceCurie-Weiss modelarm eventsfoldingsrandom-cluster representation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

A BK inequality for random matchings ⋮ Random-cluster correlation inequalities for Gibbs fields ⋮ FKG (and Other Inequalities) from (Generalized and Approximate) FK Random Cluster Representation (and Iterated Folding) ⋮ Entropy production in nonlinear recombination models ⋮ A planar Ising model of self-organized criticality

Cites Work

• Closure properties and negatively associated measures violating the Van den Berg-Kesten inequality
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• The covariance matrix of the Potts model: a random cluster analysis.
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• Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem
• Random cluster models on the triangular lattice
• Towards a theory of negative dependence
• The Dual BKR Inequality and Rudich's Conjecture
• Probability on Graphs
• Inequalities with applications to percolation and reliability
• Proof of the Van den Berg–Kesten Conjecture
• The Random-Cluster Model
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