The Annals of Applied Probability

Large deviations for combinatorial distributions. I. Central limit theorems

Hsien-Kuei Hwang

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We prove a general central limit theorem for probabilities of large deviations for sequences of random variables satisfying certain analytic conditions. This theorem has wide applications to combinatorial structures and to the distribution of additive arithmetical functions. The method of proof is an extension of Kubilius' version of Cramér's classical method based on analytic moment generating functions. We thus generalize Cramér's and Kubilius's theorems on large deviations.

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Ann. Appl. Probab. Volume 6, Number 1 (1996), 297-319.

First available in Project Euclid: 18 October 2002

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 60F10: Large deviations
Secondary: 05A16: Asymptotic enumeration 11N05: Distribution of primes 11N37: Asymptotic results on arithmetic functions

Large deviations combinatorial constructions central limit theorems additive arithmetical functions


Hwang, Hsien-Kuei. Large deviations for combinatorial distributions. I. Central limit theorems. Ann. Appl. Probab. 6 (1996), no. 1, 297--319. doi:10.1214/aoap/1034968075.

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