The Annals of Probability

The front location in branching Brownian motion with decay of mass

Louigi Addario-Berry and Sarah Penington

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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

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

Received: December 2015
Revised: August 2016
First available in Project Euclid: 27 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J65: Brownian motion [See also 58J65] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 82C22: Interacting particle systems [See also 60K35]

Branching Brownian motion branching interacting particle systems front propagation consistent maximal displacement Brownian motion


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.

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