The front location in branching Brownian motion with decay of mass

• Louigi Addario-Berry ^[1] ; Sarah Penington ^[2]
  1. [1] McGill University

     McGill University

     Canadá

     
  2. [2] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 1, 2017, págs. 3752-3794
• Idioma: inglés
• DOI: 10.1214/16-AOP1148
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• Resumen

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