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1 results

  • An example of phase transition in countable one-dimensional Markov random fields

  • Ted Cox
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 205-211
    Print publication:
    March 1977

  • Let S be a countable set, Q a strictly positive matrix on S × S. The set 𝒢(Q) of one-dimensional Markov random fields taking values in S with conditional probabilities determined by Q has been investigated by Spitzer [4], Föllmer [1] and Kesten [3]. In this paper a new result of Spitzer's is stated and proved, and used to present a specific example (the only one known) of a matrix Q which exhibits phase transition and admits a complete description of 𝒢 (Q).