25 papers
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…
Lattice random-field Widom--Rowlinson models
Benedikt Jahnel, Daniel Kamecke, Christof Külske
We consider the Widom--Rowlinson model on subject to a symmetric i.i.d.\ random field. We prove that for dimensions any non-trivial random field leads to an…
Locality properties for discrete and continuum Widom--Rowlinson models in random environments
Benedikt Jahnel, Christof Külske, Alexander Zass
We consider the Widom--Rowlinson model in which hard balls of two possible colors are constrained to a hard-core repulsion between particles of different colors, in quenched random…
Large and moderate deviations in Poisson navigations
Partha Pratim Ghosh, Benedikt Jahnel, Sanjoy Kumar Jhawar
We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme…