B. Jahnel

Comparison inequalities for discrete- and continuous-time infection processes

Benedikt Jahnel, Jonas Köppl, Pēteris Siliņš

We study comparison inequalities for contact-process-type infection dynamics on $Z^{d}$ with general local transmission mechanisms. The processes considered include both disc…

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 $Z^{d}$ subject to a symmetric i.i.d.\ random field. We prove that for dimensions $d \leq 2$ any non-trivial random field leads to an…

Restriction and mixing properties of interacting particle systems with unbounded range

Benedikt Jahnel, Jonas Köppl

We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations…

Detection, coverage and percolation in dynamic Boolean models with random radii based on $α$ -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 $α$ -stable pro…

Reversible birth-and-death dynamics in continuum: a de Bruijn-type identity for free-energy dissipation

Benedikt Jahnel, Jonas Köppl, Yannic Steenbeck +1

We investigate free-energy dissipation in a continuous-time birth-and-death dynamics in $R^{d}$ . For these Markov processes, the class of reversible measures coincides with…

Coexistence for Competing Branching Random Walks with Identical Asymptotic Shape on $Z^{d}$

Partha Pratim Ghosh, Benedikt Jahnel

We consider two independent branching random walks that start next to each other on the $d$ -dimensional hypercubic lattice and that carry two different colors. Vertices of the latt…

Local criteria for global connectivity comparisons: beyond stochastic domination

Johannes Bäumler, Benedikt Jahnel, Jonas Köppl +3

We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The…

Reversible birth-and-death dynamics in continuum: free-energy dissipation and attractor properties

Yannic Steenbeck, Alexander Zass, Jonas Köppl +1

We consider continuous-time birth-and-death dynamics in $R^{d}$ that admit at least one infinite-volume Gibbs point process based on area interactions as a reversible measur…

Functional limit theorems for edge counts in dynamic random connection hypergraphs

Christian Hirsch, Benedikt Jahnel, Péter Juhász

We introduce a dynamic random hypergraph model constructed from a bipartite graph. In this model, both vertex sets of the bipartite graph are generated by marked Poisson point proc…

Oriented bond-site percolation in random environment and contact processes with periodic recovery

Benedikt Jahnel, Lukas Lüchtrath, Anh Duc Vu

We investigate oriented bond-site percolation on the planar lattice in which entire columns are stretched. Generalising recent results by Hilário et al., we establish non-trivial p…

Throughput in inhomogeneous planar drainage networks

Partha Pratim Ghosh, Benedikt Jahnel, Yannic Steenbeck

We consider navigation schemes on planar diluted lattices and semi lattices with one discrete and one continuous component. More precisely, nodes that survive inhomogeneous Bernoul…

Phase transitions for the Widom--Rowlinson model in random environments

Benedikt Jahnel, Daniel Kamecke

We establish non-uniqueness regimes for the infinite-volume two-colored Widom--Rowlinson model based on inhomogeneous Poisson point processes with locally finite intensity measures…

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…

math.PR2024★ 1 cited

The Planar Lattice Two-Neighbor Graph Percolates

David Coupier, Benoît Henry, Benedikt Jahnel +1

The k-neighbor graph is a directed percolation model on the hypercubic lattice Z d in which each vertex independently picks exactly k of its 2d nearest neighbors at random, and we…

First contact percolation

Benedikt Jahnel, Lukas Lüchtrath, Anh Duc Vu

We study a version of first passage percolation on $Z^{d}$ where the random passage times on the edges are replaced by contact times represented by random closed sets on $\m…

Subcritical annulus crossing in spatial random graphs

Emmanuel Jacob, Benedikt Jahnel, Lukas Lüchtrath

We consider general continuum percolation models obeying sparseness, translation invariance, and spatial decorrelation. In particular, this includes models constructed on general p…

The variational principle for a marked Gibbs point process with infinite-range multibody interactions

Benedikt Jahnel, Jonas Köppl, Yannic Steenbeck +1

We prove the Gibbs variational principle for the Asakura--Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a…

math-ph2024

Gibbs measures for hardcore-SOS models on Cayley trees

Benedikt Jahnel, Utkir Rozikov

We investigate the finite-state $p$ -solid-on-solid model, for $p = \infty$ , on Cayley trees of order $k \geq 2$ and establish a system of functional equations where each solution corr…

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.…

An ergodic and isotropic zero-conductance model with arbitrarily strong local connectivity

Martin Heida, Benedikt Jahnel, Anh Duc Vu

We exhibit a percolating ergodic and isotropic lattice model in all but at least two dimensions that has zero effective conductivity in all spatial directions and for all non-trivi…

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…