The limiting distribution for the number of symbol comparisons used by QuickSort is nondegenerate (extended abstract)

TL;DR

This paper proves that the limiting distribution of the scaled number of symbol comparisons in QuickSort is nondegenerate, addressing a previously unresolved question about its nature.

Contribution

It establishes the nondegeneracy of the limiting distribution for the number of symbol comparisons in QuickSort, extending prior results.

Findings

The limiting distribution is nondegenerate.

The proof involves complex probabilistic analysis.

Addresses a gap in understanding QuickSort's behavior.

Abstract

In a continuous-time setting, Fill (2010) proved, for a large class of probabilistic sources, that the number of symbol comparisons used by QuickSort, when centered by subtracting the mean and scaled by dividing by time, has a limiting distribution, but proved little about that limiting random variable Y -- not even that it is nondegenerate. We establish the nondegeneracy of Y. The proof is perhaps surprisingly difficult.