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October 2000 Limits of logarithmic combinatorial structures
R. Arratia, A. D. Barbour, S. Tavaré
Ann. Probab. 28(4): 1620-1644 (October 2000). DOI: 10.1214/aop/1019160500

Abstract

Under very mild conditions, we prove that the limiting behavior of the component counts in a decomposable logarithmic combinatorial structure conforms to a single, unified pattern, which includes functional central limit theorems, Erdös-Turán laws, Poisson–Dirichlet limits for the large components and Poisson approximation in total variation for the total number ofcomponents. Our approach is entirely probabilistic, and the conditions can readily be verified in practice.

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R. Arratia. A. D. Barbour. S. Tavaré. "Limits of logarithmic combinatorial structures." Ann. Probab. 28 (4) 1620 - 1644, October 2000. https://doi.org/10.1214/aop/1019160500

Information

Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60003
MathSciNet: MR1813836
Digital Object Identifier: 10.1214/aop/1019160500

Subjects:
Primary: 20B25

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 4 • October 2000
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