Open Access
June 2013 Degree asymptotics with rates for preferential attachment random graphs
Erol A. Peköz, Adrian Röllin, Nathan Ross
Ann. Appl. Probab. 23(3): 1188-1218 (June 2013). DOI: 10.1214/12-AAP868


We provide optimal 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 certain distributional transformations which 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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Erol A. Peköz. Adrian Röllin. Nathan Ross. "Degree asymptotics with rates for preferential attachment random graphs." Ann. Appl. Probab. 23 (3) 1188 - 1218, June 2013.


Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1271.60019
MathSciNet: MR3076682
Digital Object Identifier: 10.1214/12-AAP868

Primary: 05C08 , 60C05 , 60F05

Keywords: preferential attachment , Random graphs , Stein’s method , urn models

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 3 • June 2013
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