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VOL. 46 | 2004 Stein’s method and non-reversible Markov chains

## Abstract

Let $W(\pi)$ be either the number of descents or inversions of a permutation $\pi \in S_n$. Stein's method is applied to show that $W$ satisfies a central limit theorem with error rate $n^{-1/2}$. The construction of an exchangeable pair $(W,W')$ used in Stein's method is non-trivial and uses a non-reversible Markov chain.

## Information

Published: 1 January 2004
First available in Project Euclid: 28 November 2007

MathSciNet: MR2118603

Digital Object Identifier: 10.1214/lnms/1196283800

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Vol. 46 • 1 January 2004