Asymptotic normality in random graphs with given vertex degrees. Issue 4 (12th January 2020)
- Record Type:
- Journal Article
- Title:
- Asymptotic normality in random graphs with given vertex degrees. Issue 4 (12th January 2020)
- Main Title:
- Asymptotic normality in random graphs with given vertex degrees
- Authors:
- Janson, Svante
- Abstract:
- Abstract: We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model and then, by a conditioning argument, for the simple uniform random graph with the given degree sequence. Such conditioning is standard for convergence in probability, but much less straightforward for convergence in distribution as here. The proof uses the method of moments, and is based on a new estimate of mixed cumulants in a case of weakly dependent variables. The result on small components is applied to give a new proof of a recent result by Barbour and Röllin on asymptotic normality of the size of the giant component in the random multigraph; moreover, we extend this to the random simple graph.
- Is Part Of:
- Random structures & algorithms. Volume 56:Issue 4(2020)
- Journal:
- Random structures & algorithms
- Issue:
- Volume 56:Issue 4(2020)
- Issue Display:
- Volume 56, Issue 4 (2020)
- Year:
- 2020
- Volume:
- 56
- Issue:
- 4
- Issue Sort Value:
- 2020-0056-0004-0000
- Page Start:
- 1070
- Page End:
- 1116
- Publication Date:
- 2020-01-12
- Subjects:
- configuration model -- asymptotic normality of giant component -- method of moments -- simple random graph -- random graph with given degrees
Random graphs -- Periodicals
Mathematical analysis -- Periodicals
519 - Journal URLs:
- http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2418 ↗
http://onlinelibrary.wiley.com/ ↗ - DOI:
- 10.1002/rsa.20905 ↗
- Languages:
- English
- ISSNs:
- 1042-9832
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 7254.411950
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 13260.xml