Open Access
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


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.


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

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

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

Vol.14 • 2009
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