Zero-one Laws for Binary Random Fields

David Coupier, Paul Doukhan and Bernard Ycart
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David Coupier: Crest
Paul Doukhan: Crest
Bernard Ycart: Crest

No 2005-47, Working Papers from Center for Research in Economics and Statistics

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.

Pages: 22
Date: 2005
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