Geodesic
An information-theoretic central limit theorem for finitely susceptible FKG systems
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 331-343

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We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of Fortuin–Kasteleyn–Ginibre (FKG) random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in what follows 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.
Keywords: entropy, Fisher information
Mots-clés : normal convergence, FKG variables. 
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     title = {An information-theoretic central limit theorem for finitely susceptible {FKG} systems},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a6/}
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O. Johnson. An information-theoretic central limit theorem for finitely susceptible FKG systems. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 331-343. http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a6/