The Annals of Probability

The front location in branching Brownian motion with decay of mass

Abstract

We augment standard branching Brownian motion by adding a competitive interaction between nearby particles. Informally, when particles are in competition, the local resources are insufficient to cover the energetic cost of motion, so the particles’ masses decay. In standard BBM, we may define the front displacement at time $t$ as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the local mass density drops from $\Theta(1)$ to $o(1)$. We show that one can find arbitrarily large times $t$ for which this occurs at a distance $\Theta(t^{1/3})$ behind the front displacement for standard BBM.

Article information

Source
Ann. Probab., Volume 45, Number 6A (2017), 3752-3794.

Dates
Revised: August 2016
First available in Project Euclid: 27 November 2017

https://projecteuclid.org/euclid.aop/1511773663

Digital Object Identifier
doi:10.1214/16-AOP1148

Mathematical Reviews number (MathSciNet)
MR3729614

Zentralblatt MATH identifier
06838106

Citation

Addario-Berry, Louigi; Penington, Sarah. The front location in branching Brownian motion with decay of mass. Ann. Probab. 45 (2017), no. 6A, 3752--3794. doi:10.1214/16-AOP1148. https://projecteuclid.org/euclid.aop/1511773663

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