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.

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.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | October 2009 |

Deposited On: | 06 Jan 2010 10:18 |

Last Modified: | 05 Apr 2016 13:31 |

Publisher: | Institute of Mathematical Statistics |

Series Name: | Adv. Texts Basler Lehrbucher |

Number of Pages: | 288 |

ISSN: | 1083-6489 |

ISBN: | 978-3-7643-9981-8 |

Official URL: | http://www.math.washington.edu/~ejpecp/viewarticle.php?id=2022&layout=abstract |

Related URLs: | http://arxiv.org/abs/0907.0347 |

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