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A functional combinatorial central limit theorem


Barbour, A D; Janson, S (2009). A functional combinatorial central limit theorem. Electronic Journal of Probability, 14:2352-2370.

Abstract

The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein's method. The pre-limiting process is then shown, under weak conditions, to converge to a Gaussian limit process. The theorem is used to describe the shape of random permutation tableaux.

Abstract

The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein's method. The pre-limiting process is then shown, under weak conditions, to converge to a Gaussian limit process. The theorem is used to describe the shape of random permutation tableaux.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:October 2009
Deposited On:06 Jan 2010 10:18
Last Modified:03 Jun 2024 01:43
Publisher:Institute of Mathematical Statistics
Series Name:Adv. Texts Basler Lehrbucher
Number of Pages:288
ISSN:1083-6489
ISBN:978-3-7643-9981-8
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/EJP.v14-709
Official URL:http://www.math.washington.edu/~ejpecp/viewarticle.php?id=2022&layout=abstract
Related URLs:http://arxiv.org/abs/0907.0347
  • Content: Published Version
  • Licence: Creative Commons: Attribution 3.0 Unported (CC BY 3.0)