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Name : Matthias Schulte
Talk Title: Large degrees in scale-free inhomogeneous random graphs
Abstract : We consider a class of random graphs whose construction involves weights and whose degree distributions follow power-laws. Examples are some long-range percolation models, the random connection model with weights, the Norros-Reittu model and the Chung-Lu model. For such random graphs we study the maximum degree in a growing observation window and show that its limiting distribution is Frechet. More generally, we establish that the point process of large degrees converges in distribution to an inhomogeneous Poisson process on the positive half-line. An important statistical question is to estimate the tail exponent of the degree distribution. Here we prove consistency of the Hill estimator.
This talk is based on joint work with Chinmoy Bhattacharjee (University of Luxembourg).
This is an invited session at EVA 2021