Random graphs; maximum degree; Hill estimator; Poisson process convergence
Résumé :
[en] 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.
Disciplines :
Mathématiques
Auteur, co-auteur :
BHATTACHARJEE, Chinmoy ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Schulte, Matthias; Hamburg University of Technology > Institute of Mathematics
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Large degrees in scale-free inhomogeneous random graphs
Date de publication/diffusion :
février 2022
Titre du périodique :
Annals of Applied Probability
ISSN :
1050-5164
Maison d'édition :
Institute of Mathematical Statistics, Etats-Unis - Ohio
