Reference : Large degrees in scale-free inhomogeneous random graphs
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Large degrees in scale-free inhomogeneous random graphs
Bhattacharjee, Chinmoy mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Schulte, Matthias mailto [Hamburg University of Technology > Institute of Mathematics]
In press
Annals of Applied Probability
Institute of Mathematical Statistics
Yes (verified by ORBilu)
[en] Random graphs ; maximum degree ; Hill estimator ; Poisson process convergence
[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.

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