On the tails of the limiting Quicksort distribution

TL;DR

This paper provides asymptotic analysis of the extreme tail behaviors of the limiting distribution of Quicksort, offering rigorous results that complement earlier non-rigorous findings.

Contribution

It presents rigorous asymptotic results for the tails of the Quicksort distribution, improving understanding of its extreme value behavior.

Findings

Asymptotic formulas for the left tail of the distribution.

Asymptotic formulas for the right tail of the distribution.

Results align with previous non-rigorous studies but are less precise.

Abstract

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.