On the tails of the limiting QuickSort density

[摘要] 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.

[学科分类] 统计和概率

[关键词] QuickSort;density tails;asymptotic bounds;Landau–Kolmogorov inequality