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A functional central limit theorem for the Ewens sampling formula

Published online by Cambridge University Press:  14 July 2016

Jennie C. Hansen
Jennie C. Hansen*
Affiliation:
Tufts University
*
∗Present address: Mathematics Department, Northeastern University, Boston, MA 02115, USA.
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Abstract

For each n > 0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integer n. To determine the limiting distributions for the part sizes of a partition with respect to the measures given by this formula, we associate to each partition a step function on [0, 1]. Each jump in the function equals the number of parts in the partition of a certain size. We normalize these functions and show that the induced measures on D[0, 1] converge to Wiener measure. This result complements Kingman's frequency limit theorem [10] for the Ewens partition structure.

Keywords

PARTITION STRUCTURESWIENER MEASURERANDOM PARTITIONSPÓLYA-LIKE URN
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 28 - 43
Copyright
Copyright © Applied Probability Trust 1990 

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