An information-theoretic Central Limit Theorem for finitely susceptible FKG systems

Details An information-theoretic Central Limit Theorem for finitely susceptible FKG systems An information-theoretic Central Limit Theorem for finitely susceptible FKG systems

2001-09-21

arxiv.org/abs/math/0109156v1

Theory of Probability and Its Applications, Vol 50/2, 2004, pages 214-224

Mathematics

Probability

17 pages

Scientific paper

10.1137/S0040585X97981676

We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in the sequel we use many of the same arguments for weakly dependent random variables. As in previous work of Barron and Johnson, we consider random variables perturbed by small normals, since the FKG property gives us control of the resulting densities. We need to impose a finite susceptibility condition -- that is, the covariance between one random variable and the sum of all the random variables should remain finite.

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