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A central limit theorem for decomposable random variables with applications to random graphs


Barbour, A D; Karonski, A (1989). A central limit theorem for decomposable random variables with applications to random graphs. Journal of Combinatorial Theory. Series B, 47(2):125-145.

Abstract

The application of Stein's method of obtaining rates of convergence to the normal distribution is illustrated in the context of random graph theory. Problems which exhibit a dissociated structure and problems which do not are considered. Results are obtained for the number of copies of a given graph G in K(n, p), for the number of induced copies of G, for the number of isolated trees of order k ≥ 2, for the number of vertices of degree d ≥ 1, and for the number of isolated vertices.

The application of Stein's method of obtaining rates of convergence to the normal distribution is illustrated in the context of random graph theory. Problems which exhibit a dissociated structure and problems which do not are considered. Results are obtained for the number of copies of a given graph G in K(n, p), for the number of induced copies of G, for the number of isolated trees of order k ≥ 2, for the number of vertices of degree d ≥ 1, and for the number of isolated vertices.

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45 citations in Web of Science®
42 citations in Scopus®
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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:1989
Deposited On:13 Apr 2010 12:38
Last Modified:05 Apr 2016 13:29
Publisher:Elsevier
ISSN:0095-8956
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/0095-8956(89)90014-2
Related URLs:http://user.math.uzh.ch/barbour/pub/Barbour/BJansonKaronskiRucinski.pdf (Author)

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