Existence and uniqueness of countable one-dimensional Markov random fields

DOI10.1214/aop/1176996027zbMath0367.60080OpenAlexW2004840609MaRDI QIDQ1242382

Harry Kesten

Publication date: 1976

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

Full work available at URL: https://doi.org/10.1214/aop/1176996027

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (14)

Classification of killed one-dimensional diffusions. ⋮ One-dimensional DLR invariant measures are regular ⋮ \(R\)-positivity of nearest neighbor matrices and applications to Gibbs states ⋮ A decision-theoretic approach for segmental classification ⋮ A variational characterization of one-dimensional countable state Gibbs random fields ⋮ DLR measures for one-dimensional harmonic systems ⋮ Champs markoviens et mesures de Gibbs sur ${R}$ ⋮ The D.L.R. conditions for translation invariant Gaussian measures on L(R d) ⋮ The age functional for Markov chains ⋮ Hamiltonians on random walk trajectories ⋮ A consistent system of conditional probabilities which is not compatible with any random field ⋮ On the absence of phase transition in one-dimensional random fields ⋮ Some old and new problems in thermodynamic formalism of infinite state Markov chains ⋮ Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice

This page was built for publication: Existence and uniqueness of countable one-dimensional Markov random fields