Author:
Bovier Anton,Hartung Lisa
Abstract
AbstractWe consider a model of branching Brownian motion with self-repulsion. Self-repulsion is introduced via a change of measure that penalises particles spending time in an $$\epsilon $$
ϵ
-neighbourhood of each other. We derive a simplified version of the model where only branching events are penalised. This model is almost exactly solvable, and we derive a precise description of the particle numbers and branching times. In the limit of weak penalty, an interesting universal time-inhomogeneous branching process emerges. The position of the maximum is governed by a F-KPP type reaction-diffusion equation with a time-dependent reaction term.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics