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Critical branching Brownian motion with absorption: Particle configurations

  • Author(s): Berestycki, J;
  • Berestycki, N;
  • Schweinsberg, J
  • et al.

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.

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