11 papers · 1 filter
Phase transitions for contact processes on sparse random graphs via metastability and local limits
Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch
We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise t…
Cluster sizes in subcritical soft Boolean models
Benedikt Jahnel, Lukas Lüchtrath, Marcel Ortgiese
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.…
Convex order and faster transmission in first contact percolation
Benedikt Jahnel, Jonas Köppl, Lukas Lüchtrath +1
Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in f…
Age-dependent random connection models with arc reciprocity: clustering and connectivity
Lukas Lüchtrath, Christian Mönch
We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{re…
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…