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Nonstandard regular variation of in-degree and out-degree in the preferential attachment model. (English) Zbl 1343.60138

Summary: For the directed edge preferential attachment network growth model studied by B. Bollobás et al. [in: Proceedings of the 14th annual ACM-SIAM symposium on discrete algorithms, SODA 2003, Baltimore, MD, USA, January 12–14, 2003. New York, NY: Association for Computing Machinery; Philadelphia, PA: Society for Industrial and Applied Mathematics. 132–139 (2003; Zbl 1094.68605)] and P. L. Krapivsky and S. Redner [“Organization of growing random networks”, Phys. Rev. E (3) 63, No. 6, Article ID 066123 (2001; doi:10.1103/PhysRevE.63.066123)], 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
05C80 Random graphs (graph-theoretic aspects)
60G70 Extreme value theory; extremal stochastic processes

Citations:

Zbl 1094.68605
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Full Text: DOI arXiv Euclid

References:

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