ON THE POISSON-DIRICHLET LIMIT

Kingman showed that if the vector X-N is distributed according to the Dirichlet law then the vector of descending order statistics converges , under certain conditions, to a nondegenerate limit. This contrasts w ith the fact that the limit of any fixed component of X-N is zero. Nev ertheless, X-N does have, in some sense, a nondegenerate limit which w e identify with a random interval partition. Convergence of this kind does not require rearranging of the components and implies the existen ce of limit distributions for a class of functionals which are not cov ered by the Kingman result. (C) 1998 Academic Press