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arXiv · 2102.07128

Branching Brownian motion with self repulsion

Anton Bovier·Lisa Hartung
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Abstract

We consider a model of branching Brownian motion with self repulsion. Self-repulsion is introduced via change of measure that penalises particles spending time in an $\e$-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.

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Anton Bovier, Lisa Hartung. 2021-02-14. Branching Brownian motion with self repulsion. https://arxiv.org/abs/2102.07128

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