Smoothness and decay properties of the limiting Quicksort density function
<|reference_start|>Smoothness and decay properties of the limiting Quicksort density function: 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.<|reference_end|>
@article{fill2000smoothness,
    title={Smoothness and decay properties of the limiting Quicksort density
  function},
    author={James Allen Fill (Johns Hopkins Univ.), Svante Janson (Uppsala Univ.)},
    journal={arXiv preprint arXiv:math/0005235},
    year={2000},
    number={601, Department of Mathematical Sciences, The Johns Hopkins
  University},
    archivePrefix={arXiv},
    eprint={math/0005235},
    primaryClass={math.PR cs.DS}
}