FRANK BALL frank.ball@nottingham.ac.uk
Professor of Applied Probability
The asymptotic variance of the giant component of configuration model random graphs
Ball, Frank; Neal, Peter
Authors
PETER NEAL Peter.Neal@nottingham.ac.uk
Professor of Statistics
Abstract
For a supercritical configuration model random graph it is well known that, subject to mild conditions, there exists a unique giant component, whose size $R_n$ is $O (n)$, where $n$ is the total number of vertices in the random graph. Moreover, there exists $0 < \rho \leq 1$ such that $R_n/n \convp \rho$ as $\nr$. We show that for a sequence of {\it well-behaved} configuration model random graphs with a deterministic degree sequence satisfying $0 < \rho < 1$, there exists $\sigma^2 > 0$, such that $var (\sqrt{n} (R_n/n -\rho)) \rightarrow \sigma^2$ as $\nr$. Moreover, an explicit, easy to compute, formula is given for $\sigma^2$. This provides a key stepping stone for computing the asymptotic variance of the size of the giant component for more general random graphs.
Citation
Ball, F., & Neal, P. (2017). The asymptotic variance of the giant component of configuration model random graphs. Annals of Applied Probability, 27(2), https://doi.org/10.1214/16-AAP1225
Journal Article Type | Article |
---|---|
Acceptance Date | Jun 15, 2016 |
Publication Date | May 26, 2017 |
Deposit Date | Jun 22, 2016 |
Publicly Available Date | May 26, 2017 |
Journal | Annals of Applied Probability |
Print ISSN | 1050-5164 |
Electronic ISSN | 1050-5164 |
Publisher | Institute of Mathematical Statistics (IMS) |
Peer Reviewed | Peer Reviewed |
Volume | 27 |
Issue | 2 |
DOI | https://doi.org/10.1214/16-AAP1225 |
Keywords | Random graphs, configuration model, branching processes, variance |
Public URL | https://nottingham-repository.worktribe.com/output/861887 |
Publisher URL | http://projecteuclid.org/euclid.aoap/1495764374 |
Contract Date | Jun 22, 2016 |
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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