%0 Journal Article
%T Regenerative partition structures
%A Alexander Gnedin
%A Jim Pitman
%J Mathematics
%D 2004
%I arXiv
%X We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random subset of the positive halfline, that is the closed range of a subordinator. A general regenerative partition structure is thus represented in terms of the Laplace exponent of an associated subordinator. We also analyse deletion properties characteristic of the two-parameter family of partition structures.
%U http://arxiv.org/abs/math/0408071v1