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 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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Journal of Applied Probability
Tinbergen Institute

G. Samarodnitsky (Gennady), Resnick, S.I, D. Towsley (Don), R.A. Davis (Richard), A. Willis (Amy), & Wan, P. (2016). Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. Journal of Applied Probability, 53(1), 146–161. Retrieved from