# Central Limit Theorems for Weakly Dependent Random Fields

• Alexander Bulinski
• Evgeny Spodarev
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2068)

## Abstract

This chapter is a primer on the limit theorems for dependent random fields. First, dependence concepts such as mixing, association and their generalizations are introduced. Then, moment inequalities for sums of dependent random variables are stated which yield e.g. the asymptotic behaviour of the variance of these sums which is essential for the proof of limit theorems. Finally, central limit theorems for dependent random fields are given. Applications to excursion sets of random fields and Newman’s conjecture in the absence of finite susceptibility are discussed as well.

## Keywords

Random Field Central Limit Theorem Dependent Random Variable Gaussian Random Field Dependence Concept
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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