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Joint degree distributions of preferential attachment random graphs

  • Erol Peköz (a1), Adrian Röllin (a2) and Nathan Ross (a3)

We study the joint degree counts in linear preferential attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p and also provide optimal rates of convergence of the finite-dimensional distributions. The results hold for models with any general initial seed graph and any fixed number of initial outgoing edges per vertex; we generate nontree graphs using both a lumping and a sequential rule. Convergence of the order statistics and optimal rates of convergence to the maximum of the degrees is also established.

Corresponding author
* Postal address: Questrom School of Business, Boston University, 595 Commonwealth Avenue, Room 607, Boston, MA 02215, USA. Email address:
** Postal address: Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore. Email address:
*** Postal address: School of Mathematics and Statistics, University of Melbourne, Richard Berry Building, VIC 3010, Australia. Email address:
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Advances in Applied Probability
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  • EISSN: 1475-6064
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