# Branching Brownian Motion with Self-Repulsion

Annales Henri Poincaré（2022）

Abstract

We 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 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.

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Key words

brownian motion,self

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