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Asymptotic normality of degree counts in a preferential attachment model

Published online by Cambridge University Press:  25 July 2016

Sidney I. Resnick*
Affiliation:
Cornell University
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: [email protected]
School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: [email protected]

Abstract

Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference, for instance GLM techniques, and model-verification methods will require knowing test statistics are asymptotically normal even though node- or count-based network data are nothing like classical data from independently replicated experiments. We therefore study asymptotic normality of degree counts for a sequence of growing simple undirected preferential attachment graphs. The methods of proof rely on identifying martingales and then exploiting the martingale central limit theorems.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2016 

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