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November 2017 The front location in branching Brownian motion with decay of mass
Louigi Addario-Berry, Sarah Penington
Ann. Probab. 45(6A): 3752-3794 (November 2017). DOI: 10.1214/16-AOP1148


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.


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Louigi Addario-Berry. Sarah Penington. "The front location in branching Brownian motion with decay of mass." Ann. Probab. 45 (6A) 3752 - 3794, November 2017.


Received: 1 December 2015; Revised: 1 August 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 06838106
MathSciNet: MR3729614
Digital Object Identifier: 10.1214/16-AOP1148

Primary: 60J80
Secondary: 60J65 , 60J70 , 82C22

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

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6A • November 2017
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