LARGE DEVIATIONS FOR THE DEGREE STRUCTURE IN PREFERENTIAL ATTACHMENT SCHEMES

• 成果类型: Article
• 署名作者: Choi, Jihyeok; Sethuraman, Sunder
• 署名单位: Syracuse University; University of Arizona
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP854
• 发表日期: 2013
• 页码: 722-763
• 关键词: NETWORKS; time

摘要

Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path evolution of the empirical degree distribution is found by Dupuis-Ellis-type methods. Interestingly, the rate function, which can be evaluated, contains a term which accounts for the cost of assigning a fraction of the total degree to an infinite degree component, that is, when an atypical condensation effect occurs with respect to the degree structure. As a consequence of the large deviation results, a sample path a.s. law of large numbers for the degree distribution is deduced in terms of a coupled system of ODEs from which power law bounds for the limiting degree distribution are given. However, by analyzing the rate function, one can see that the process can deviate to a variety of atypical nonpower law distributions with finite cost, including distributions typically associated with sub and superlinear selection models.