Degree asymptotics with rates for preferential attachment random graphs

Details Degree asymptotics with rates for preferential attachment random graphs Degree asymptotics with rates for preferential attachment random graphs

2011-08-26

arxiv.org/abs/1108.5236v1

Mathematics

Probability

29 pages

Scientific paper

We provide rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed points of a certain distributional transformation that allows us to obtain rates of convergence using a new variation of Stein's method. Despite the large literature on these models, there is surprisingly little known about the limiting distributions so we also provide some properties and new representations including an explicit expression for the densities in terms of the confluent hypergeometric function of the second kind.

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