Sharp large deviations and concentration inequalities for the number of descents in a random permutation
Probability
2024-11-20 v2
Abstract
The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin-Hall distribution, we prove that the number of descents satisfies a sharp large deviation principle. A very precise concentration inequality involving the rate function in the large deviation principle is also provided.
Keywords
Cite
@article{arxiv.2210.10382,
title = {Sharp large deviations and concentration inequalities for the number of descents in a random permutation},
author = {Bernard Bercu and Michel Bonnefont and Adrien Richou},
journal= {arXiv preprint arXiv:2210.10382},
year = {2024}
}