Abstract

The Ewens sampling formula is a family of measures on permutations, that arises in population genetics, Bayesian statistics and many other applications. This family is indexed by a parameter ; the usual uniform measure is included as the special case . Under the Ewens sampling formula with parameter , the process of cycle counts converges to a Poisson process with independent coordinates and . Exploiting a particular coupling, we give simple explicit upper bounds for the Wasserstein and total variation distances between the laws of and . This Poisson approximation can be used to give simple proofs of limit theorems with bounds for a wide variety of functionals of such random permutations.