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 | References | Similar Articles | Additional Information

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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Additional Information

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