Stein's Method and Non-Reversible Markov Chains
Probability
2007-05-23 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.math/9712241,
title = {Stein's Method and Non-Reversible Markov Chains},
author = {Jason Fulman},
journal= {arXiv preprint arXiv:math/9712241},
year = {2007}
}
Comments
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