Zero-one laws for binary random fields
Probability
2007-05-23 v1 Logic
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 , the threshold functions of local propositions are computed, and sufficient conditions for the zero-one law are given.
Keywords
Cite
@article{arxiv.math/0605502,
title = {Zero-one laws for binary random fields},
author = {David Coupier and Paul Doukhan and Bernard Ycart},
journal= {arXiv preprint arXiv:math/0605502},
year = {2007}
}
Comments
16 pages, 1 figure. Keywords: zero-one law, first-order logic, random field, weak dependence, Ising model