# A central limit theorem for a new statistic on permutations

@article{Chatterjee2016ACL, title={A central limit theorem for a new statistic on permutations}, author={Sourav Chatterjee and Persi Diaconis}, journal={Indian Journal of Pure and Applied Mathematics}, year={2016}, volume={48}, pages={561-573} }

This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving central limit theorems more generally. It gives us an opportunity to acknowledge the work of our teacher and friend B. V. Rao.

## 31 Citations

### A central limit theorem for the two-sided descent statistic on Coxeter groups

- 2019

Mathematics

We study the asymptotic behaviour of the statistic (des+ ides)W which assigns to an element w of a finite Coxeter group W the number of descents of w plus the number of descents of w. Our main result…

### A Central Limit Theorem for the number of descents and some urn models

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The purpose of this work is to establish a central limit theorem that can be applied to a particular form of Markov chains, including the number of descents in a random permutation of…

### A Central Limit Theorem for Vincular Permutation Patterns

- 2017

Mathematics

Discret. Math. Theor. Comput. Sci.

It is shown that this statistics on uniform random permutations is asymptotically normal and described the speed of convergence and to prove this central limit theorem, the method of dependency graphs is used.

### A Central Limit Theorem for the Two-Sided Descent Statistic on Coxeter Groups

- 2022

Mathematics

Electron. J. Comb.

We study the asymptotic behaviour of the statistic $(\operatorname{des}+\operatorname{ides})_W$ which assigns to an element $w$ of a finite Coxeter group $W$ the number of descents of $w$ plus the…

### Sharp large deviations and concentration inequalities for the number of descents in a random permutation

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Mathematics

. 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…

### Central limit theorem for descents in conjugacy classes of Sn

- 2020

Mathematics

J. Comb. Theory, Ser. A

### On the central limit theorem for the two-sided descent statistics in Coxeter groups

- 2020

Mathematics

Electronic Communications in Probability

In 2018, Kahle and Stump raised the following problem: identify sequences of finite Coxeter groups $W_n$ for which the two-sided descent statistics on a uniform random element of $W_n$ is…

### A central limit theorem for descents of a Mallows permutation and its inverse

- 2022

Mathematics

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation $w$, and its inverse, distributed according to the Mallows measure. The Mallows measure is a non-uniform…

### A Berry-Esseen Bound for Nonlinear Statistics with Bounded Differences

- 2021

Mathematics

Statistics, Optimization & Information Computing

In this paper, we obtain an explicit Berry-Esseen bound in the central limit theorem for nonlinear statistics with bounded differences. Some examples are provided as well.

### Asymptotics of a locally dependent statistic on finite reflection groups

- 2018

Mathematics

This paper discusses the asymptotic behaviour of the number of descents in a random signed permutation and its inverse, which was listed as an interesting direction by Chatterjee and Diaconis (2017).…

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