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 Θ(1) to o(1). We show that one can find arbitrarily large times t for which this occurs at a distance Θ(t1/3) behind the front displacement for standard BBM.
Original language  English 

Pages (fromto)  37523794 
Number of pages  43 
Journal  Annals of Probability 
Volume  45 
Issue number  6A 
Early online date  27 Nov 2017 
DOIs  
Publication status  Published  30 Nov 2017 
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Sarah Penington
 Department of Mathematical Sciences  Lecturer & Royal Society Research Fellow
 Probability Laboratory at Bath
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching, Researcher