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Smoothness and decay properties of the limiting Quicksort density function

James Allen Fill·Svante Janson
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Abstract

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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James Allen Fill, Svante Janson. 2000-05-23. Smoothness and decay properties of the limiting Quicksort density function. https://arxiv.org/abs/math/0005235

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