Publisher DOI: 10.1214/21-AAP1693
Title: LARGE DEGREES IN SCALE-FREE INHOMOGENEOUS RANDOM GRAPHS
Language: English
Authors: Bhattacharjee, Chinmoy 
Schulte, Matthias 
Keywords: Hill estimator; maximum degree; Poisson process convergence; Random graphs
Issue Date: Feb-2022
Source: Annals of Applied Probability 32 (1) : 696-720 (2022-02)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/12119
ISSN: 1050-5164
Journal: The annals of applied probability 
Institute: Mathematik E-10 
Document Type: Article
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