Journal of Applied Probability

Nonstandard regular variation of in-degree and out-degree in the preferential attachment model

Gennady Samorodnitsky, Sidney Resnick, Don Towsley, Richard Davis, Amy Willis, and Phyllis Wan

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For the directed edge preferential attachment network growth model studied by Bollobás et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails. Typically, the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular variation is nonstandard. Only marginal regular variation has been previously established for this distribution in the cases where the marginal tail indices are different.

Article information

J. Appl. Probab., Volume 53, Number 1 (2016), 146-161.

First available in Project Euclid: 8 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes 05C80: Random graphs [See also 60B20]

Multivariate heavy tails preferential attachment model scale-free networks


Samorodnitsky, Gennady; Resnick, Sidney; Towsley, Don; Davis, Richard; Willis, Amy; Wan, Phyllis. Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. J. Appl. Probab. 53 (2016), no. 1, 146--161.

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