Stein's Method and Non-Reversible Markov Chains

Abstract

Let W be either the number of descents or inversions of a permutation. 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.

9 pages; final version appearing in IMS Lecture Notes, Volume 46 "Stein's Method: Expository Lectures and Applications". Change in title, slightly better bounds and exposition, updated bibliography