4 papers
A sharp survival threshold for branching Brownian motion in a self-generated resource environment
Maciej Głuchowski, Georg Menz
We study branching Brownian motion in a resource environment created by the particles themselves. Particles reproduce at rate times the resource nearby, resource is consumed at…
Ergodicity Criterion for One-Sided, One-Dimensional IPS with a Long-Lived State
Maciej Gluchowski, Georg Menz
We study one-dimensional, one-sided, nearest-neighbor Interacting Particle Systems (IPS) with positive rates and identify a criterion for ergodicity based on the presence of a long…
A correlation bound for the one-dimensional heterogeneous Ising model
Edward Athaide, Maciej Głuchowski, Jonas Köppl +1
We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay…
Time-Scaling, Ergodicity and Covariance Decay of Interacting Particle Systems
Maciej Głuchowski, Georg Menz
The main focus of this article is the study of ergodicity of Interacting Particle Systems (IPS). We present a simple lemma showing that scaling time is equivalent to taking the con…