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.
"On the tails of the limiting QuickSort density." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP213