Asymptotic behavior of some statistics in Ewens random permutations

Details Asymptotic behavior of some statistics in Ewens random permutations Asymptotic behavior of some statistics in Ewens random permutations

2012-01-10

arxiv.org/abs/1201.2157v2

Mathematics

Probability

Version 2 is an extended abstract of 12 pages. For the full paper (36 pages), see version 1

Scientific paper

The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We describe the asymptotic behavior of a large family of statistics, including the number of occurrences of any given dashed pattern. Our approach is based on the method of moments and relies on the following intuition: two events involving the images of different integers are almost independent.

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