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Limits of logarithmic combinatorial structures


Arratia, R; Barbour, A D; Tavaré, S (2000). Limits of logarithmic combinatorial structures. The Annals of Probability, 28(4):1620-1644.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2000
Deposited On:07 Apr 2010 12:32
Last Modified:05 Apr 2016 13:25
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Publisher DOI:https://doi.org/10.1214/aop/1019160500

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