An example on the central limit theorem for associated sequences
\textit{C. M. Newman} [Commun. Math. Phys. 74, 119-128 (1980; Zbl 0429.60096)] and \textit{C. M. Newman} and \textit{A. L. Wright} [Ann. Probab. 9, 671-675 (1981; Zbl 0465.60009)] conjectured that the central limit theorem holds for strictly stationary associated sequences \((X_ n)\) with \(K(R)=Var(X_ 1)+2\sum^{R}_{j=2}Cov(X_ 1,X_ j)\) slowly varying as \(R\to \infty\). The content of this paper is a counterexample to this conjecture.
scientific article; zbMATH DE number 3866281