and
by James Allen Fill, Svante Janson
http://www.mts.jhu.edu/~fill/papers/quick_fix.ps
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Abstract:
The limiting distribution of the normalized number of key comparisons required by the Quicksort sorting algorithm is known to be the unique fixed point of a certain distributional transformation T---unique, that is, subject to the constraints of zero mean and finite variance. We show that a distribution is a fixed point of T if and only if it is the convolution of with a Cauchy distribution of arbitrary center and scale. In particular, therefore, is the unique fixed point of T having zero mean.
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