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https://doi.org/10.1214/12-AAP868
Title: | Degree asymptotics with rates for preferential attachment random graphs | Authors: | Peköz, E.A. Röllin, A. Ross, N. |
Keywords: | Preferential attachment Random graphs Stein's method Urn models |
Issue Date: | Jun-2013 | Citation: | Peköz, E.A., Röllin, A., Ross, N. (2013-06). Degree asymptotics with rates for preferential attachment random graphs. Annals of Applied Probability 23 (3) : 1188-1218. ScholarBank@NUS Repository. https://doi.org/10.1214/12-AAP868 | Abstract: | 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. © 2013 Institute of Mathematical Statistics. | Source Title: | Annals of Applied Probability | URI: | http://scholarbank.nus.edu.sg/handle/10635/105081 | ISSN: | 10505164 | DOI: | 10.1214/12-AAP868 |
Appears in Collections: | Staff Publications |
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