Peter Mörters

Percolation phase transition in weight-dependent random connection models

We investigate spatial random graphs defined on the points
of a Poisson process in d-dimensional space, which combine scale-free
degree distributions and long-range effects. Every Poisson point is
assigned an independent weight. Given the weight and position of the points, we
form an edge between any pair of points independently with a
probability depending on the two weights of the points and their
distance. Preference is given to short edges and connections to
vertices with large weights. We characterize the parameter regime
where there is a nontrivial percolation phase transition and show that
it depends not only on the power-law exponent of the degree
distribution but also on a geometric model parameter. Based on joint
work with Peter Gracar and Lukas Luechtrath.