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

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

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arXiv · 1405.4882

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

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

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Abstract

For the directed edge preferential attachment network growth model studied by Bollobas 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 non-standard. Only marginal regular variation has been previously established for this distribution in the cases where the marginal tail indices are different.

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Gennady Samorodnitsky, Sidney Resnick, Don Towsley, Richard Davis, Amy Willis, Phyllis Wan. 2014-05-19. Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. https://arxiv.org/abs/1405.4882

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