The Annals of Applied Probability

On the Functional Central Limit Theorem for the Ewens Sampling Formula

Peter Donnelly, Thomas G. Kurtz, and Simon Tavare

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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


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