LARGE DEGREES IN SCALE-FREE INHOMOGENEOUS RANDOM GRAPHS

• 成果类型: Article
• 署名作者: Bhattacharjee, Chinmoy; Schulte, Matthias
• 署名单位: University of Luxembourg; Hamburg University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1693
• 发表日期: 2022
• 页码: 696-720
• 关键词: distance; GROWTH

摘要

We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet. We achieve this by proving convergence of the underlying point process of the degrees to a certain Poisson process. Estimating the index of the power-law tail for the typical degree distribution is an important question in statistics. We prove consistency of the Hill estimator for the inverse of the tail exponent of the typical degree distribution.