Journal article
Joint degree distributions of preferential attachment random graphs
E Peköz, A Röllin, N Ross
Advances in Applied Probability | Cambridge University Press (CUP) | Published : 2017
DOI: 10.1017/apr.2017.5
Abstract
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.
Grants
Awarded by Automotive Research Center
Funding Acknowledgements
We thank Jim Pitman for the suggestion to study joint degree distributions for preferential attachment graphs and for pointers to the CRT literature, Sourav Chatterjee for the suggestion to look at the order statistics of the process, Rongfeng Sun for helpful discussions, and the anonymous referees for their valuable comments. E. P. thanks the Department of Mathematics and Statistics at the University of Melbourne for their hospitality during a visit when much of this work was completed, supported by a UofM ECR grant. A.R. was supported by NUS Research Grant R-155-000-124-112. N. R. was supported by ARC grant DP150101459.