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July 1997 The representation of composition structures
Alexander V. Gnedin
Ann. Probab. 25(3): 1437-1450 (July 1997). DOI: 10.1214/aop/1024404519


A composition structure is a sequence of consistent probability distributions for compositions (ordered partitions) of $n = 1, 2, \dots$. Any composition structure can be associated with an exchangeable random composition of the set of natural numbers. Following Donnelly and Joyce, we study the problem of characterizing a generic composition structure as a convex mixture of the "extreme" ones. We topologize the family $\mathscr{U}$ of open subsets of [0, 1] so that $\mathscr{U}$ becomes compact and show that $\mathscr{U}$ is homeomorphic to the set of extreme composition structures. The general composition struc-ture is related to a random element of $\mathscr{U}$ via a construction introduced by J. Pitman.


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Alexander V. Gnedin. "The representation of composition structures." Ann. Probab. 25 (3) 1437 - 1450, July 1997.


Published: July 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0895.60037
MathSciNet: MR1457625
Digital Object Identifier: 10.1214/aop/1024404519

Primary: 60G09
Secondary: 60C05 , 60J50

Keywords: Composition structure , exchangeability , paintbox process , partition structure , random set

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • July 1997
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