1973/08/01 by C.J. Preston · 47 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Markov Chains and Monte Carlo Methods #Mathematics #Markov chain #Random field #Statistical physics #Random graph #Markov model #Nearest neighbour #Markov process #Markov kernel #Variable-order Markov model #Markov property #Graph #Combinatorics #Discrete mathematics #Statistics #Computer science #Artificial intelligence #Physics
paper · doi:10.2307/1426035
published in Advances in Applied Probability 5(2), 242-261 (Cambridge University Press)
openalex publication_date 1973/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/24
It is shown that the set of Markov random fields and Gibbs states with nearest neighbour potentials are the same for any finite graph. The set of Markov random fields is also shown to be the same as the equilibrium states of time-reversible birth/death processes with nearest neighbour interactions defined on the graph.