Electronic Journal of Probability

A Functional Combinatorial Central Limit Theorem

Andrew Barbour and Svante Janson

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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.

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 81, 2352-2370.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 60F17: Functional limit theorems; invariance principles 62E20: Asymptotic distribution theory 05E10: Combinatorial aspects of representation theory [See also 20C30]

Gaussian process combinatorial central limit theorem permutation tableau Stein's method

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Barbour, Andrew; Janson, Svante. A Functional Combinatorial Central Limit Theorem. Electron. J. Probab. 14 (2009), paper no. 81, 2352--2370. doi:10.1214/EJP.v14-709. https://projecteuclid.org/euclid.ejp/1464819542

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