The purpose of this article is to present a general method to fin limiting laws for some renormalized statistics on random permutations. The model of random permutations considered here is Ewens sampling model, which generalizes uniform random permutations. Under this model, we describe the asymptotic behavior of some statistics, including the number of occurrences of any 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.
"Asymptotic behavior of some statistics in Ewens random permutations." Electron. J. Probab. 18 1 - 32, 2013. https://doi.org/10.1214/EJP.v18-2496