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math.PR2022
The contact process on scale-free geometric random graphs
Peter Gracar, Arne Grauer
We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on . This class includes th…
math.PR2022★ 2 cited
Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension
Peter Gracar, Lukas Lüchtrath, Christian Mönch
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large we…