DIRICHLET-KINGMAN PARTITION REVISITED

Thierry Huillet (France) and Servet Martinez (Chile)

Received January 9, 2007

Abstract

We reconsider the Dirichlet model for the random division of an interval. This model is parameterized by  number of fragments, together with a set of positive parameters  Its main remarkable properties are recalled, developed and illustrated. Explicit results on the statistical structure of its size-biased permutation are then obtained. This distribution appears in the sorting of items problem under the move-to-front rule. Assuming the parameters satisfy  as  it is shown that the Dirichlet distribution has a Dirichlet-Kingman non-degenerate weak limit whose properties are briefly outlined.

Keywords and phrases: random discrete distribution, asymmetric Dirichlet partition, size-biased permutation, gamma subordinator, Dirichlet-Kingman partition.