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Generalized Gibbs states and Markov random fields

  • C. J. Preston (a1)
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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[1] Averintsev, M. B. (1970) On a method of describing discrete parameter random fields. Problemy Peredachi Informatsii 6, 100109.
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[3] Bartlett, M. S. (1972) Physical nearest-neighbor models and non-linear time series. II. Further discussion of approximate solutions and exact equations. J. Appl. Prob. 9, 7686.
[4] Hammersley, J. M. and Clifford, P. Markov fields on finite graphs and lattices. Unpublished.
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[7] Spitzer, F. (1971) Markov random fields and Gibbs ensembles. Amer. Math. Monthly 78, 142154.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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