Phase separation in random cluster models. II: The droplet at equilibrium, and local deviation lower bounds

DOI10.1214/11-AOP646zbMath1271.60021arXiv1001.1528MaRDI QIDQ428136

Alan Hammond

Publication date: 19 June 2012

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1528

zbMATH Keywords

phase separationrandom cluster modelWulff constructionlocal roughness

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

Related Items

The competition of roughness and curvature in area-constrained polymer models, Isoperimetry in Two-Dimensional Percolation, Modulus of continuity for polymer fluctuations and weight profiles in Poissonian last passage percolation, Phase separation in random cluster models. III: Circuit regularity, Local and global geometry of the 2D Ising interface in critical prewetting, Phase separation in random cluster models. I: Uniform upper bounds on local deviation, Gibbs measures on permutations over one-dimensional discrete point sets

Cites Work

• Phase separation in random cluster models. III: Circuit regularity
• The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\)
• Phase separation in random cluster models. I: Uniform upper bounds on local deviation
• Interfaces in the Potts model. I: Pirogov-Sinai theory of the Fortuin- Kasteleyn representation
• Fluctuation theory of connectivities for subcritical random cluster models
• On the supremum of a certain Gaussian process
• Dobrushin-Kotecký-Shlosman theorem up to the critical temperature
• On weak mixing in lattice models
• Lower bounds for boundary roughness for droplets in Bernoulli percolation
• Sharpness of the phase transition in percolation models
• On the Wulff crystal in the Ising model.
• Mixing properties and exponential decay for lattice systems in finite volumes.
• Airy distribution function: from the area under a Brownian excursion to the maximal height of fluctuating interfaces
• Kac's formula, levy's local time and brownian excursion
• Dynamic Scaling of Growing Interfaces
• Some conditional correlation inequalities for percolation and related processes
• Cube-root boundary fluctuations for droplets in random cluster models
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item