A functional combinatorial central limit theorem
2009 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 14, 2352-2370 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2009. Vol. 14, 2352-2370 p.
Gaussian process, combinatorial central limit theorem, permutation tableau, Stein's method
IdentifiersURN: urn:nbn:se:uu:diva-114389ISI: 000272621000003OAI: oai:DiVA.org:uu-114389DiVA: diva2:293877