On the exponential decay of the characteristic function of the quicksort distribution

TL;DR

This paper proves that the characteristic function of the quicksort distribution decays exponentially at infinity, enabling the analytical extension of its density near the real line.

Contribution

It establishes the exponential decay of the characteristic function of the quicksort distribution, a novel result with implications for its density's analytical properties.

Findings

Characteristic function decays exponentially at infinity

Density can be analytically extended near the real line

Provides new insights into the distribution's properties

Abstract

We prove that the characteristic function of the quicksort distribution is exponentially decreasing at infinity. As a consequence it follows that the density of the quicksort distribution can be analytically extended to the vicinity of the real line.