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A Characterization of GEM Distributions

Published online by Cambridge University Press:  25 June 2001

ALEXANDER GNEDIN  and
SERGEI KEROV
ALEXANDER GNEDIN
Affiliation:
School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne NE1 7RU, England (e-mail: Alexander.Gnedin@ncl.ac.uk)
SERGEI KEROV
Affiliation:
Steklov Mathematical Institute at St. Petersburg (POMI), Fontanka 27, St. Petersburg, 191011, Russia (e-mail: kerov@pdmi.ras.ru)
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Abstract

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Let (Xn) be a residual allocation model with i.i.d. residual fractions Un: For W a random variable with values in [0; 1] and independent of (Xn), we define another sequence (Yn) by setting

(formula here)

Under minor regularity assumptions we show that (Xn) and (Yn) have the same probability law if and only if this law is a GEM distribution. In this case, the distribution of W and the Uns is Beta(1; θ) for some θ > 0.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 3 , May 2001 , pp. 213 - 217
Copyright
2001 Cambridge University Press