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 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 …

We show that for long-range percolation with polynomially decaying connection probabilities
in dimension $ d\geq 2$, the critical value depends continuously on the precise …

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 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 …

This note provides a sufficient condition for linear lower bounds on chemical distances
(compared to the Euclidean distance) in general spatial random graphs. The condition is …

Consider independent long-range percolation on $\mathbb {Z}^ d $ for $ d\geq 3$.
Assuming that the expected degree of the origin is infinite, we show that there exists an …

We provide a sufficient criterion for the recurrence of spatial random graphs on the real line
based on the scarceness of long-edges. In particular, this complements earlier recurrence …