Regenerative partition structures

Alexander Gnedin; Jim Pitman

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Regenerative partition structures

Alexander Gnedin·Jim Pitman

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Abstract

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.

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Alexander Gnedin, Jim Pitman. 2004-08-04. Regenerative partition structures. https://arxiv.org/abs/math/0408071

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