This article is cited in 4 papers

An information-theoretic central limit theorem for finitely susceptible FKG systems

O. Johnson

Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge

Abstract: 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: normal convergence, entropy, Fisher information, FKG variables.

Received: 12.10.2001

Language: English

DOI: 10.4213/tvp110

 English version: Theory of Probability and its Applications, 2006, 50:2, 214–224

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