2 citations · 2 across the 8 of their papers we have counts for
10 papers
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…
Maximising homomorphism counts between digraphs
Lukas Lüchtrath, Christian Mönch
We prove a Sidorenko-type inequality for directed trees: for every oriented tree on vertices and every finite directed graph , the homomorphism count hom is bound…
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 pro…
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…
Phase transitions for contact processes on one-dimensional networks
Benedikt Jahnel, Lukas Lüchtrath, Christian Mönch
We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the…
First contact percolation
Benedikt Jahnel, Lukas Lüchtrath, Anh Duc Vu
We study a version of first passage percolation on where the random passage times on the edges are replaced by contact times represented by random closed sets on $\m…
The Erdős-Rényi Random Graph Conditioned on Every Component Being a Clique
Martijn Gösgens, Lukas Lüchtrath, Elena Magnanini +2
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can…
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.…
Existence of subcritical percolation phases for generalised weight-dependent random connection models
Benedikt Jahnel, Lukas Lüchtrath
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…