UC San Diego
Critical branching Brownian motion with absorption: Particle configurations
- Author(s): Berestycki, J
- Berestycki, N
- Schweinsberg, J
- et al.
Published Web Locationhttps://doi.org/10.1214/14-AIHP613
© Association des Publications de l'Institut Henri Poincaré, 2015. We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x > 0, particles move according to independent one-dimensional Brownian motions with the critical drift of -√2, and particles are absorbed when they reach zero. Here we obtain asymptotic results concerning the behavior of the process before the extinction time, as the position x of the initial particle tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle. We also obtain asymptotic results for the configuration of particles at a typical time.