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.Comment: 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
