DEGREE ASYMPTOTICS WITH RATES FOR PREFERENTIAL ATTACHMENT RANDOM GRAPHS

• 成果类型: Article
• 署名作者: Pekoez, Erol A.; Roellin, Adrian; Ross, Nathan
• 署名单位: Boston University; National University of Singapore; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP868
• 发表日期: 2013
• 页码: 1188-1218
• 关键词: theorems

摘要

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.