Electronic Communications in Probability

On the tails of the limiting QuickSort density

James Allen Fill and Wei-Chun Hung

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Abstract

We give upper and lower asymptotic bounds for the left tail and for the right tail of the continuous limiting QuickSort density $f$ that are nearly matching in each tail. The bounds strengthen results from a paper of Svante Janson (2015) concerning the corresponding distribution function $F$. Furthermore, we obtain similar bounds on absolute values of derivatives of $f$ of each order.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 7, 11 pp.

Dates
Received: 2 August 2018
Accepted: 19 January 2019
First available in Project Euclid: 14 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1550113298

Digital Object Identifier
doi:10.1214/19-ECP213

Subjects
Primary: 68P10: Searching and sorting
Secondary: 60E05: Distributions: general theory 60C05: Combinatorial probability

Keywords
QuickSort density tails asymptotic bounds Landau–Kolmogorov inequality

Rights
Creative Commons Attribution 4.0 International License.

Citation

Fill, James Allen; Hung, Wei-Chun. On the tails of the limiting QuickSort density. Electron. Commun. Probab. 24 (2019), paper no. 7, 11 pp. doi:10.1214/19-ECP213. https://projecteuclid.org/euclid.ecp/1550113298


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References

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