We investigate random graphs on the points of a Poisson process in d-dimensional space,
which combine scale-free degree distributions and long-range effects. Every Poisson point …

We study cluster sizes in supercritical $ d $-dimensional inhomogeneous percolation
models with long-range edges--such as long-range percolation--and/or heavy-tailed degree …

We consider a random connection model (RCM) on a general space driven by a Poisson
process whose intensity measure is scaled by a parameter $ t\ge 0$. We say that the infinite …

One-dependent first passage percolation is a spreading process on a graph where the
transmission time through each edge depends on the direct surroundings of the edge. In …

We study geometric random graphs defined on the points of a Poisson process in d-
dimensional space, which additionally carry independent random marks. Edges are …

We consider a large class of spatially-embedded random graphs that includes among others
long-range percolation, continuum scale-free percolation and the age-dependent random …

We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an
iid weight and edges are drawn such that short edges and edges to vertices with large …

We derive a sufficient condition for the existence of a subcritical percolation phase for a wide
range of continuum percolation models where each vertex is embedded into Euclidean …

Here we prove critical exponents for Random Connections Models (RCMs) with random
marks. The vertices are given by a marked Poisson point process on R d and an edge exists …

Abstract Let X 1, X 2,… be iid random variables with values in Z d satisfying PX 1= x= PX
1=− x= Θ‖ x‖− s for some s> d. We show that the random walk defined by S n=∑ k= 1 n X …