Large Deviations of Combinatorial Distributions I: Central Limit Theorems
نویسنده
چکیده
We prove a general central limit theorem for probabilities of large deviations for sequences of random variables satisfying certain natural 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’ theorems on large deviations. AMS 1991 subject classifications. Primary 60F10, 60F10; secondary 60C05, 11K65.
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