Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice

DOI10.1016/0304-4149(85)90213-3zbMath0585.60056OpenAlexW1980700367MaRDI QIDQ1070653

Stan Zachary

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0304-4149(85)90213-3

zbMATH Keywords

infinite treesexistence and uniqueness of Markov random fields

Mathematics Subject Classification ID

Random fields (60G60) Markov processes (60J99)

Related Items (20)

Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree ⋮ Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree ⋮ Limiting Gibbs measures of Potts model with countable set of spin values ⋮ Nonmonotonicity of phase transitions in a loss network with controls ⋮ A new set of limiting Gibbs measures for the Ising model on a Cayley tree ⋮ The Potts model with countable set of spin values on a Cayley tree ⋮ On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three ⋮ Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree ⋮ A Three State Hard-Core Model on a Cayley Tree ⋮ Extremality of translation-invariant phases for a three-state SOS-model on the binary tree ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ QUANTUM MARKOV FIELDS ON GRAPHS ⋮ Gradient Gibbs measures for the SOS model with countable values on a Cayley tree ⋮ Periodic Gibbs measures for the Potts-SOS model on a Cayley tree ⋮ Fertile HC models with three states on a Cayley tree ⋮ Extremality of translation-invariant Gibbs measures for the Potts–SOS model on the Cayley tree ⋮ ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO ⋮ Uniqueness of quantum Markov chains associated with an \(XY\)-model on a Cayley tree of order 2 ⋮ Stem and topological entropy on Cayley trees ⋮ GIBBS MEASURES FOR SOS MODELS ON A CAYLEY TREE

Cites Work

• Countable state space Markov random fields and Markov chains on trees
• Markov random fields on an infinite tree
• Phase transition in one-dimensional nearest-neighbor systems
• Existence and uniqueness of countable one-dimensional Markov random fields
• Sufficient statistics and extreme points
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