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A convergence theorem for symmetric functionals of random partitions
Published online by Cambridge University Press: 14 July 2016
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 → ∞.
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- Copyright © Applied Probability Trust 1992
Footnotes
The authors were supported in part by NSF grant DMS90-05833.
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