A functional combinatorial central limit theorem

2009/07/02 by A. D. Barbour, Svante Janson, Barbour, A. D. +1
Computer Science · Mathematics · #05E10 #60C05 #60F17 #62E20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:05E10 #msc:60C05 #msc:60F17 #msc:62E20

paper · pdf · doi:10.48550/arxiv.0907.0347

23 pages

arxiv created 2009/07/02 · openalex publication_date 2009/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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