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Asymptotic normality of degree counts in a preferential attachment model

Part of: Stochastic processes Graph theory

Published online by Cambridge University Press:  25 July 2016

Sidney I. Resnick  and
Gennady Samorodnitsky
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]
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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.

Keywords

Preferential attachmentsocial networkheavy tailsasymptotic normality

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 05C80: Random graphs
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 283 - 299
Copyright
Copyright © Applied Probability Trust 2016 

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