易受扰动FKG系统的信息论中心极限定理
An information-theoretic Central Limit Theorem for finitely susceptible FKG systems
摘要：
我们适应参数熵理论的收敛性从独立的情况下，FKG随机变量的情况下。选择FKG系统是因为它们的相关性结构仅通过协方差控制，尽管在后面我们对弱相关随机变量使用许多相同的参数。在Barron和Johnson以前的工作中，我们考虑了受小法线扰动的随机变量，因为FKG性质使我们能够控制所得的密度。我们需要施加一个有限的易感性条件--也就是说，一个随机变量与所有随机变量之和之间的协方差应该保持有限。
英文摘要：
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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