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Markov fields with polygonal realizations
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  • Published: February 1989

Markov fields with polygonal realizations

  • T. Arak1 &
  • D. Surgailis2 

Probability Theory and Related Fields volume 80, pages 543–579 (1989)Cite this article

  • 98 Accesses

  • 30 Citations

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Summary

We define a new class of Markov random fields with two-dimensional parameter z∈T⊂ℝ2, which take a finite number of values separated by random polygonal boundaries. In some special cases, these random fields are consistent in T and allow and alternative description in terms of the equilibrium evolution of a system of one-dimensional particles.

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References

  1. Arak, T.: On Markovian random fields with finite number of values. 4th USSR-Japan symposium on probability theory and mathematical statistics. Abstracts of communications, Tbilisi 1982

  2. Kendall, M.G., Moran, P.A.P.: Geometrical probability. New York: Hafner 1963

    Google Scholar 

  3. Rozanov, Ju.A.: Markov random fields. Moscow: Nauka 1981

    Google Scholar 

  4. Ruelle, D.: Statistical mechanics. New York: Benjamin 1969

    Google Scholar 

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Author information

Authors and Affiliations

  1. Tartu University, 202400, Tartu, Estonia, USSR

    T. Arak

  2. Institute of Mathematics and Cybernetics, 232600, Vilnius, Lithuania, USSR

    D. Surgailis

Authors
  1. T. Arak
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  2. D. Surgailis
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Cite this article

Arak, T., Surgailis, D. Markov fields with polygonal realizations. Probab. Th. Rel. Fields 80, 543–579 (1989). https://doi.org/10.1007/BF00318906

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  • Received: 10 February 1987

  • Revised: 18 April 1988

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00318906

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Keywords

  • Stochastic Process
  • Probability Theory
  • Finite Number
  • Statistical Theory
  • Random Field
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