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On the Poisson-Dirichlet Limit

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  • Gnedin, Alexander V.

Abstract

Kingman showed that if the vectorXNis distributed according to the Dirichlet law then the vector of descending order statistics converges, under certain conditions, to a nondegenerate limit. This contrasts with the fact that the limit of any fixed component ofXNis zero. Nevertheless,XNdoes have, in some sense, a nondegenerate limit which we identify with a random interval partition. Convergence of this kind does not require rearranging of the components and implies the existence of limit distributions for a class of functionals which are not covered by the Kingman result.

Suggested Citation

  • Gnedin, Alexander V., 1998. "On the Poisson-Dirichlet Limit," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 90-98, October.
  • Handle: RePEc:eee:jmvana:v:67:y:1998:i:1:p:90-98
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