The Quicksort Process

TL;DR

This paper analyzes the stochastic process of Quicksort as it sorts real numbers, showing that the normalized process converges to a limiting cadlag process as the number of elements increases.

Contribution

It introduces a probabilistic process perspective of Quicksort's runtime and proves weak convergence to a limiting process in the space of cadlag functions.

Findings

Normalized Quicksort process converges weakly to a limiting process.

The limiting process has cadlag paths.

Provides a new probabilistic framework for analyzing Quicksort.

Abstract

Quicksort on the fly returns the input of $n$ reals in increasing natural order during the sorting process. Correctly normalized the running time up to returning the l-th smallest out of n seen as a process in l converges weakly to a limiting process with path in the space of cadlag functions.