We give asymptotics for the left and right tails of the limiting Quicksort distribution. The results agree with, but are less precise than, earlier non-rigorous results by Knessl and Spankowski.
"On the tails of the limiting Quicksort distribution." Electron. Commun. Probab. 20 1 - 7, 2015. https://doi.org/10.1214/ECP.v20-4525