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2000 A Characterization of the Set of Fixed Points of the Quicksort Transformation
James Fill, Svante Janson
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Electron. Commun. Probab. 5: 77-84 (2000). DOI: 10.1214/ECP.v5-1021


The limiting distribution $\mu$ 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 $\mu$ with a Cauchy distribution of arbitrary center and scale. In particular, therefore, $\mu$ is the unique fixed point of $T$ having zero mean.


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James Fill. Svante Janson. "A Characterization of the Set of Fixed Points of the Quicksort Transformation." Electron. Commun. Probab. 5 77 - 84, 2000.


Accepted: 26 May 2000; Published: 2000
First available in Project Euclid: 2 March 2016

zbMATH: 0943.68192
MathSciNet: MR1781841
Digital Object Identifier: 10.1214/ECP.v5-1021

Keywords: Characteristic function , coupling , domain of attraction , fixed point , integral equation , QuickSort , Smoothing transformation


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