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A convergence theorem for symmetric functionals of random partitions

Part of: Combinatorial probability Limit theorems

Published online by Cambridge University Press:  14 July 2016

Paul Joyce  and
Simon Tavaré
Paul Joyce*
Affiliation:
University of Idaho
Simon Tavaré*
Affiliation:
University of Southern California
*
∗Postal address: Department of Mathematics and Statistics, University of Idaho, Moscow, ID 83843, USA.
∗∗Postal address: Department of Mathematics, University of Southern California, Los Angeles, CA 90089–1113, USA.
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Abstract

This paper gives general conditions under which symmetric functionals of random partitions of the integer m converge in distribution as m → ∞. The main result is used to settle a conjecture of Donnelly et al. (1991) to the effect that the mean of the sum of the square roots of the relative sizes of the components of a random mapping of m integers converges to π/2 as m → ∞.

Keywords

RANDOM MAPPINGSRANDOM PERMUTATIONSPOISSON–DIRICHLET DISTRIBUTION

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F05: Central limit and other weak theorems 92D10: Genetics
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 280 - 290
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

The authors were supported in part by NSF grant DMS90-05833.

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