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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 60G09
Secondary: 60C05, 60J50

Rights: Copyright © 1997 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.25 • No. 3 • July 1997
Back to Top