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Proceedings of the American Mathematical Society

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Markov property of extremal local fields

Authors: N. Dang-Ngoc and G. Royer
Journal: Proc. Amer. Math. Soc. 70 (1978), 185-188
MSC: Primary 60J99; Secondary 60K35
MathSciNet review: 0478385
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Abstract: We show that extremal local field on $ {(E,\mathcal{E})^T}$, with $ T = {\mathbf{Z}}$ or R and $ (E,\mathcal{E})$ standard, possesses the Markov property. This result generalizes that of F. Spitzer in the case $ T = {\mathbf{Z}}$, E countable and a result of G. Royer and M. Yor on extremal measures associated to certain diffusion processes.

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  • [1] N. Dang Ngoc and M. Yor, Champs markoviens et mesures de Gibbs sur 𝑅, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 1, 29–69 (French, with English summary). MR 504421
  • [2] H. Föllmer, Phase transition and Martin boundary, Séminaire Probabilités Strasbourg IX, Lecture Notes in Math., Springer-Verlag, Berlin and New York, 1976.
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  • [5] Frank Spitzer, Phase transition in one-dimensional nearest-neighbor systems, J. Functional Analysis 20 (1975), no. 3, 240–255. MR 0388583

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Keywords: Markov field, local Markov field, Markov process, Markov property, Gibbs state
Article copyright: © Copyright 1978 American Mathematical Society