On the Functional Central Limit Theorem for the Ewens Sampling Formula

Abstract

The Ewens sampling formula arises in population genetics and the study of random permutations as a probability distribution on the set of partitions (by allelic type in a sample, or according to cycle structure, respectively) of the integer $n$ for each $n$. It may be embedded naturally in the familiar linear birth process with immigration. One consequence of this is another proof of the functional central limit theorem for the Ewens sampling formula.