Smoothness and decay properties of the limiting Quicksort density function

Details Smoothness and decay properties of the limiting Quicksort density function Smoothness and decay properties of the limiting Quicksort density function

2000-05-23

arxiv.org/abs/math/0005235v1

Mathematics

Probability

11 pages. Refereed article, to apppear in a book edited by D. Gardy and A. Mokkadem and published in 2000 by Birkhauser

Scientific paper

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.

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