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. 
James Allen Fill (Johns Hopkins Univ.), Svante Janson (Uppsala Univ.)