A functional central limit theorem for the Ewens sampling formula
- 1 March 1990
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 27 (1) , 28-43
- https://doi.org/10.2307/3214593
Abstract
For eachn> 0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integern. 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 onD[0, 1] converge to Wiener measure. This result complements Kingman's frequency limit theorem [10] for the Ewens partition structure.Keywords
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