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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Generalized Szegő theorems and asymptotics of cumulants by graphical methods


Author: Florin Avram
Journal: Trans. Amer. Math. Soc. 330 (1992), 637-649
MSC: Primary 60F05
DOI: https://doi.org/10.1090/S0002-9947-1992-1059708-X
MathSciNet review: 1059708
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Abstract: We obtain some general asymptotics results about a class of deterministic sums called "sums with dependent indices," which generalize a classical theorem of Szegö. The above type of sums is encountered when establishing convergence to the Gaussian distribution of sums of Wick products by the method of cumulants. Our asymptotic results reduce in this situation the proof of the central limit theorem to the study of the connectivity of a family of associated graphs.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1059708-X
Keywords: Power counting conditions, generalized Hölder inequality, Szegö theorem, bond matroid, diagram formulae
Article copyright: © Copyright 1992 American Mathematical Society