Joint degree distributions of preferential attachment random graphs

2014/02/19 by Erol A. Peköz, Peköz, Erol A., Adrian Röllin +3
Mathematics · #05C80 #60B12 #60F05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:05C80 #msc:60B12 #msc:60F05

paper · pdf · doi:10.48550/arxiv.1402.4686

20 pages

arxiv created 2016/12/08 · arxiv updated 2016/12/09

Abstract

We study the joint degree counts in proportional 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 non-tree 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.

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