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Zero-one Laws for Binary Random Fields

Author

Listed:
  • David Coupier

    (Crest)

  • Paul Doukhan

    (Crest)

  • Bernard Ycart

    (Crest)

Abstract

A set of binary random variables indexed by a lattice torus is considered. Under a mixing hypothesis, the probability of any proposition belonging to the first order logic of colored graphs tends to 0 or 1, as the size of the lattice tends to infinity. For the particular case of the Ising model with bounded pair potential and surface potential tending to -8, the threshold functions of local propositions are computed, and sufficient conditions for the zero-one law are given.

Suggested Citation

  • David Coupier & Paul Doukhan & Bernard Ycart, 2005. "Zero-one Laws for Binary Random Fields," Working Papers 2005-47, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-47
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    References listed on IDEAS

    as
    1. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
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