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.

Additional Metadata
Keywords multivariate heavy tails, preferential attachment model, scale free networks
Persistent URL hdl.handle.net/1765/112200
Journal Journal of Applied Probability
Citation
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 http://hdl.handle.net/1765/112200