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Large degrees in scale-free inhomogeneous random graphs
Publikationstyp
Journal Article
Date Issued
2022-02
Sprache
English
Author(s)
Institut
Volume
32
Issue
1
Start Page
696
End Page
720
Citation
Annals of Applied Probability 32 (1): 696-720 (2022-02)
Publisher DOI
Scopus ID
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.
Subjects
Hill estimator
maximum degree
Poisson process convergence
Random graphs