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

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...

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Bibliographic Details
Published inJournal of combinatorial theory. Series B Vol. 47; no. 2; pp. 125 - 145
Main Authors Barbour, A.D, Karoński, Michal, Ruciński, Andrzej
Format Journal Article
LanguageEnglish
Published Duluth, MN Elsevier Inc 01.10.1989
Academic Press
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Limit theorems
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Convergence rate
Central limit theorem
Random graph
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Summary: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.
ISSN:0095-8956
1096-0902
DOI:10.1016/0095-8956(89)90014-2