## The Annals of Applied Probability

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

### On the Functional Central Limit Theorem for the Ewens Sampling Formula

Peter Donnelly, Thomas G. Kurtz, and Simon Tavare

#### 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

**Subjects**

Primary: 60C05: Combinatorial probability

Secondary: 60F17: Functional limit theorems; invariance principles 60J85: Applications of branching processes [See also 92Dxx] 92D10: Genetics {For genetic algebras, see 17D92}

**Keywords**

Random partitions random permutations Brownian motion

#### 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