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Generalized Gibbs States and Markov Random Fields

C. J. Preston
Advances in Applied Probability
Vol. 5, No. 2 (Aug., 1973), pp. 242-261
DOI: 10.2307/1426035
Stable URL: http://www.jstor.org/stable/1426035
Page Count: 20
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Generalized Gibbs States and Markov Random Fields
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Abstract

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.

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