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On Poisson–Dirichlet Limits for Random Decomposable Combinatorial Structures

Published online by Cambridge University Press:  01 May 1999

RICHARD ARRATIA ,
A. D. BARBOUR  and
SIMON TAVARÉ
RICHARD ARRATIA
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, USA (e-mail: rarratia@math.usc.edustavare@gnome.usc.edu)
A. D. BARBOUR
Affiliation:
Abteilung für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland (e-mail: adb@amath.unizh.ch)
SIMON TAVARÉ
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, USA (e-mail: rarratia@math.usc.edustavare@gnome.usc.edu)
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Abstract

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We prove a joint local limit law for the distribution of the r largest components of decomposable logarithmic combinatorial structures, including assemblies, multisets and selections. Our method is entirely probabilistic, and requires only weak conditions that may readily be verified in practice.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 3 , May 1999 , pp. 193 - 208
Copyright
1999 Cambridge University Press