Smoothness and decay properties of the limiting Quicksort density function

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

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Probability, Data Structures and Algorithms, 68W40 (primary), 68P10, 60E05, 60E10 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/59268

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0005235
 http://arxiv.org/abs/math/0005235

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arXiv