On the Poisson-Dirichlet Limit

Alexander V. Gnedin

Journal of Multivariate Analysis, 1998, vol. 67, issue 1, 90-98

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.

Keywords: Poisson-Dirichlet; limit; exchangeable; interval; partition (search for similar items in EconPapers)
Date: 1998
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