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Poisson Representation of a Ewens Fragmentation Process

Published online by Cambridge University Press:  01 November 2007

ALEXANDER GNEDIN  and
JIM PITMAN
ALEXANDER GNEDIN
Affiliation:
Mathematical Institute, Utrecht University, The Netherlands (e-mail: gnedin@math.uu.nl
JIM PITMAN
Affiliation:
Department of Statistics, University of California, Berkeley, USA (e-mail: pitman@stat.Berkeley.EDU)
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Abstract

A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [n] = 1,. . .,n at time θ ≥ 0 is governed by the Ewens sampling formula with parameter θ. These partition-valued processes are exchangeable and consistent, as n varies. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx−1dx on/mathbbR+, arranged to beintensifying as θ increases.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 6 , November 2007 , pp. 819 - 827
Copyright
Copyright © Cambridge University Press 2007

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