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A functional combinatorial central limit theorem. (English) Zbl 1193.60010
Summary: 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.

MSC:
60C05 Combinatorial probability
60F17 Functional limit theorems; invariance principles
62E20 Asymptotic distribution theory in statistics
05A16 Asymptotic enumeration
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