4 papers
The q-model category of multipointed d-spaces is not left proper
Philippe Gaucher
We prove that the q-model category of -multipointed d-spaces for is not left proper by constructing a weak equivalence whose pu…
Detection, coverage and percolation in dynamic Boolean models with random radii based on -stable processes
Peter Gracar, Benedikt Jahnel, Lukas Lüchtrath +1
We consider a dynamic network in continuum time and space in which nodes, with initial locations given by a Poisson point process, move according to i.i.d. isotropic -stable pr…
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…
Chemical distance in the Poisson Boolean model with regularly varying diameters
Peter Gracar, Marilyn Korfhage
We study the Poisson Boolean model with convex bodies which are rotation-invariant distributed. We assume that the convex bodies have regularly varying diameters with indices $-α_…