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See detailLarge degrees in scale-free inhomogeneous random graphs
Bhattacharjee, Chinmoy UL; Schulte, Matthias

in Annals of Applied Probability (in press)

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 ... [more ▼]

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. [less ▲]

Detailed reference viewed: 31 (1 UL)
See detailGaussian approximation in random minimal directed spanning trees
Bhattacharjee, Chinmoy UL

E-print/Working paper (2021)

Detailed reference viewed: 28 (2 UL)
See detailGaussian approximation for sums of region-stabilizing scores
Bhattacharjee, Chinmoy UL; Molchanov, Ilya

E-print/Working paper (2021)

Detailed reference viewed: 28 (2 UL)