Asymptotic behavior of some statistics in Ewens random permutations
Probability
2013-10-28 v5 Combinatorics
Abstract
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.
Cite
@article{arxiv.1201.2157,
title = {Asymptotic behavior of some statistics in Ewens random permutations},
author = {Valentin Féray},
journal= {arXiv preprint arXiv:1201.2157},
year = {2013}
}
Comments
32 pages: final version for EJP, produced by the author. An extended abstract of 12 pages, published in the proceedings of AofA 2012, is also available as version 3