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.

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.

## Citations

## Altmetrics

## 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: | 10.1016/0095-8956(89)90014-2 |

Related URLs: | http://user.math.uzh.ch/barbour/pub/Barbour/BJansonKaronskiRucinski.pdf (Author) |

## Download

Full text not available from this repository.View at publisher

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.