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A note on applications of the martingale central limit theorem to random permutations

✍ Scribed by Chern-Ching Chao

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 160 KB
Volume: 10
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199705)10:3<323::aid-rsa2>3.0.co;2-y

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✦ Synopsis

A unified martingale approach is presented for establishing the asymptotic normality of some sequences of random variables. It is applied to the numbers of inversions, rises, and peaks, respectively, as well as the oscillation and the sum of consecutive pair products of a random permutation.

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