### Percolation phase transition in weight-dependent random connection models

Probability Seminar

5th February 2021, 3:15 pm – 4:15 pm

Online,

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.

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