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A Characterization of the Set of Fixed Points of the Quicksort Transformation


 
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1. Title Title of document A Characterization of the Set of Fixed Points of the Quicksort Transformation
 
2. Creator Author's name, affiliation, country James Allen Fill; The Johns Hopkins University
 
2. Creator Author's name, affiliation, country Svante Janson; Uppsala University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Quicksort, fixed point, characteristic function, smoothing transformation,domain of attraction, coupling, integral equation
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2000-05-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1021
 
10. Identifier Digital Object Identifier 10.1214/ECP.v5-1021
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 5
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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