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Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes


Bertoin, Jean (2008). Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes. Combinatorics, Probability & Computing, 17(3):329-337.

Abstract

We show that for $0<\alpha<1$ and $\theta>-\alpha$, the Poisson-Dirichlet distribution with parameter $(\alpha, \theta)$ is the unique reversible distribution of a rather natural fragmentation-coalescence process. This completes earlier results in the literature for certain split and merge transformations and the parameter $\alpha =0$.

Abstract

We show that for $0<\alpha<1$ and $\theta>-\alpha$, the Poisson-Dirichlet distribution with parameter $(\alpha, \theta)$ is the unique reversible distribution of a rather natural fragmentation-coalescence process. This completes earlier results in the literature for certain split and merge transformations and the parameter $\alpha =0$.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:29 May 2013 15:30
Last Modified:07 Dec 2017 21:15
Publisher:Cambridge University Press
ISSN:0963-5483
Publisher DOI:https://doi.org/10.1017/S0963548307008784
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2410390
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1165.60032
http://arxiv.org/abs/0704.3122

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