Smoothness and decay properties of the limiting Quicksort density function
概率论
2007-05-23 v1 数据结构与算法
摘要
Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere positive and infinitely differentiable density f, and that each derivative f^{(k)} enjoys superpolynomial decay at plus and minus infinity. In particular, each f^{(k)} is bounded. Our method is sufficiently computational to prove, for example, that f is bounded by 16.
引用
@article{arxiv.math/0005235,
title = {Smoothness and decay properties of the limiting Quicksort density function},
author = {James Allen Fill and Svante Janson},
journal= {arXiv preprint arXiv:math/0005235},
year = {2007}
}
备注
11 pages. Refereed article, to apppear in a book edited by D. Gardy and A. Mokkadem and published in 2000 by Birkhauser