On the Functional Central Limit Theorem for the Ewens Sampling Formula

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.