Central Limit Theorems for Weakly Dependent Random Fields

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


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.


Random Field Central Limit Theorem Dependent Random Variable Gaussian Random Field Dependence Concept 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Ulm UniversityUlmGermany

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