Electronic Communications in Probability

On the tails of the limiting QuickSort density

James Allen Fill and Wei-Chun Hung

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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

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

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

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Digital Object Identifier

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

QuickSort density tails asymptotic bounds Landau–Kolmogorov inequality

Creative Commons Attribution 4.0 International License.


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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