A Stein ' s Method Proof of the Asymptotic Normality of Descents and Inversions in theSymmetric
نویسنده
چکیده
Let W ( ) be either the number of descents or inversions of a permutation 2 Sn. Stein's method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the rst use of Stein's method in theory of permutation statistics. The construction of an exchangeable pair (W;W 0) used in Stein's method is non-trivial and may be of independent interest. 2
منابع مشابه
Stein ’ s Method Proof of the Asymptotic Normality of Descents and Inversions in the Symmetric Group By Jason
Let W (π) be either the number of descents or inversions of a permutation π ∈ Sn. Stein’s method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the first use of Stein’s method in theory of permutation statistics. The construction of an exchangeable pair (W,W ) used in Stein’s method is non-trivial and may be of in...
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