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2009 A Functional Combinatorial Central Limit Theorem
Andrew Barbour, Svante Janson
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Electron. J. Probab. 14: 2352-2370 (2009). DOI: 10.1214/EJP.v14-709

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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Andrew Barbour. Svante Janson. "A Functional Combinatorial Central Limit Theorem." Electron. J. Probab. 14 2352 - 2370, 2009. https://doi.org/10.1214/EJP.v14-709

Information

Accepted: 30 October 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1193.60010
MathSciNet: MR2556014
Digital Object Identifier: 10.1214/EJP.v14-709

Subjects:
Primary: 60C05
Secondary: 05E10, 60F17, 62E20

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Vol.14 • 2009
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