The Annals of Applied Probability

Degree asymptotics with rates for preferential attachment random graphs

Erol A. Peköz, Adrian Röllin, and Nathan Ross

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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.

Article information

Source
Ann. Appl. Probab. Volume 23, Number 3 (2013), 1188-1218.

Dates
First available in Project Euclid: 7 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1362684858

Digital Object Identifier
doi:10.1214/12-AAP868

Mathematical Reviews number (MathSciNet)
MR3076682

Zentralblatt MATH identifier
1271.60019

Subjects
Primary: 60C05: Combinatorial probability 60F05: Central limit and other weak theorems 05C08

Keywords
Random graphs preferential attachment Stein’s method urn models

Citation

Peköz, Erol A.; Röllin, Adrian; Ross, Nathan. Degree asymptotics with rates for preferential attachment random graphs. Ann. Appl. Probab. 23 (2013), no. 3, 1188--1218. doi:10.1214/12-AAP868. https://projecteuclid.org/euclid.aoap/1362684858.


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