Sharp large deviations and concentration inequalities for the number of descents in a random permutation (Q6617597)

In this paper the authors further study the asymptotic bahavior of the number of decents \((D_n)\) in a random permutation of \(\{1, \dots, n\}\). More precisely, they obtain a sharp large deviation principle for \((D_n)\) and establish an optimal concentration inequality involving the rate function of the large deviation principle. They provide two different approaches to prove these results. The first approach is based on martingales and the second approach relies on a link between the distribution of \((D_n)\) and the Irwin-Hall distribution. The second approach is more direct, while the first approach is more robust.