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Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing

Part of: Combinatorial probability Limit theorems

Published online by Cambridge University Press:  14 July 2016

Larry Goldstein
Larry Goldstein*
Affiliation:
University of Southern California
*
∗Postal address: Department of Mathematics, University of Southern California, 3620 Vermont Avenue, KAP 108, Los Angeles, CA 90089-2532, USA. Email address: larry@math.usc.edu
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Abstract

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Berry-Esseen-type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated in an application to combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points. The size biasing bounds are applied to the occurrences of fixed, relatively ordered subsequences (such as rising sequences) in a random permutation, and to the occurrences of patterns, extreme values, and subgraphs in finite graphs.

Keywords

Smoothing inequalityStein's methodpermutationgraph

MSC classification

Primary: 60F05: Central limit and other weak theorems 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 661 - 683
Copyright
© Applied Probability Trust 2005 

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