Scaling Limits for Associated Random Measures

Abstract

The problem of estimating $\operatorname{Prob}(X(B) \leq x)$ for large regions $B \subset \mathbb{R}^d$ when $X$ is a random measure is solved under a condition of positive dependence and summable correlations. Several applications are given and, in cases in which the applications have been examined previously, it is shown that the results are true under milder moment conditions than known before.