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 …

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 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 study a general class of percolation models in Euclidean space including long-range
percolation, scale-free percolation, the weight-dependent random connection model and …

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 …

We investigate a spatial random graph model whose vertices are given as a marked
Poisson process on $\mathbb {R}^ d $. Edges are inserted between any pair of points …

We study a general class of inhomogeneous spatial random graphs, the weight-dependent
random connection model. Vertices are given through a standard Poisson point process in …

We consider the soft Boolean model, a model that interpolates between the Boolean model
and long-range percolation, where vertices are given via a stationary Poisson point process …

We consider general continuum percolation models obeying sparseness, translation
invariance, and spatial decorrelation. In particular, this includes models constructed on …