## The Annals of Applied Probability

### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 1, Number 4 (1991), 539-545.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005837

Digital Object Identifier
doi:10.1214/aoap/1177005837

Mathematical Reviews number (MathSciNet)
MR1129773

Zentralblatt MATH identifier
0747.60013

JSTOR
links.jstor.org

#### Citation

Donnelly, Peter; Kurtz, Thomas G.; Tavare, Simon. On the Functional Central Limit Theorem for the Ewens Sampling Formula. Ann. Appl. Probab. 1 (1991), no. 4, 539--545. doi:10.1214/aoap/1177005837. https://projecteuclid.org/euclid.aoap/1177005837