## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### Stein’s method and non-reversible Markov chains

Jason Fulman

#### 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.

#### Chapter information

Source
Persi Diaconis and Susan Holmes, eds., Stein's Method: Expository Lectures and Applications (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004) , 66-74

Dates
First available in Project Euclid: 28 November 2007

https://projecteuclid.org/euclid.lnms/1196283800

Digital Object Identifier
doi:10.1214/lnms/1196283800

Mathematical Reviews number (MathSciNet)
MR2118603

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