THE FRONT LOCATION IN BRANCHING BROWNIAN MOTION WITH DECAY OF MASS

• 成果类型: Article
• 署名作者: Addario-Berry, Louigi; Penington, Sarah
• 署名单位: McGill University; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1148
• 发表日期: 2017
• 页码: 3752-3794
• 关键词: traveling-waves; survival; equation

摘要

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.