Coloring percolation clusters at random.

DOI10.1016/S0304-4149(01)00115-6zbMath1058.60090OpenAlexW2076121320MaRDI QIDQ1766017

Olle Häggström

Publication date: 25 February 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(01)00115-6

zbMATH Keywords

bond percolationGibbs measurerandom-cluster modelpositive correlationsquasilocality

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35)

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Cites Work

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• Random walks and percolation on trees
• An upper bound on the critical percolation probability for the three- dimensional cubic lattice
• On the uniqueness of the infinite occupied cluster in dependent two- dimensional site percolation
• The critical probability of bond percolation on the square lattice equals 1/2
• Random walks, capacity and percolation on trees
• Gibbs measures and phase transitions
• Domination by product measures
• The number of infinite clusters in dynamical percolation
• Indistinguishability of percolation clusters
• Positive correlations in the fuzzy Potts model
• Almost sure quasilocality in the random cluster model.
• Almost sure quasilocality fails for the random-cluster model on a tree.
• Almost Gibbsian versus weakly Gibbsian measures
• A uniqueness condition for Gibbs measures, with application to the 2- dimensional Ising antiferromagnet
• Graphical representations for Ising systems in external fields
• Infinite clusters in percolation models
• Uniform spanning forests
• The Ising model on diluted graphs and strong amenability
• Random-cluster measures and uniform spanning trees
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• Phase transitions on nonamenable graphs
• Gibbs states of graphical representations of the Potts model with external fields
• Probability on Trees and Networks
• Percolation
• Exact sampling with coupled Markov chains and applications to statistical mechanics