On the Tails of the Limiting QuickSort Density

Authors James Allen Fill, Wei-Chun Hung

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Author Details

James Allen Fill
  • Department of Applied Mathematics and Statistics, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218-2682, USA
Wei-Chun Hung
  • Department of Applied Mathematics and Statistics, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218-2682, USA

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James Allen Fill and Wei-Chun Hung. On the Tails of the Limiting QuickSort Density. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 21:1-21:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 upper bounds on absolute values of derivatives of f of each order.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
  • Mathematics of computing → Distribution functions
  • Quicksort
  • density tails
  • asymptotic bounds
  • Landau-Kolmogorov inequality


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