Sharp Large Deviations for the Number of Descents and the Major Index in a Random Permutation

TL;DR

This paper establishes sharp large deviation principles of any order for the number of descents and the major index in random permutations, improving the understanding of their tail behaviors.

Contribution

It introduces a comprehensive framework for sharp large deviations of any order for key permutation statistics, extending previous results.

Findings

Sharp large deviation principles of any order for descents

Sharp large deviation principles of any order for the major index

Enhanced understanding of tail behaviors in permutation statistics

Abstract

The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of any order for the major index in a random permutation.