English

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}
}