Hyperbolic branching Brownian motion

@article{Lalley1997HyperbolicBB,
  title={Hyperbolic branching Brownian motion},
  author={Steven P. Lalley and T. Sellke},
  journal={Probability Theory and Related Fields},
  year={1997},
  volume={108},
  pages={171-192}
}
  • Steven P. Lalley, T. Sellke
  • Published 1997
  • Mathematics
  • Probability Theory and Related Fields
  • Summary. Hyperbolic branching Brownian motion is a branching diffusion process in which individual particles follow independent Brownian paths in the hyperbolic plane ?2, and undergo binary fission(s) at rate λ > 0. It is shown that there is a phase transition in λ: For λ≦ 1/8 the number of particles in any compact region of ?2 is eventually 0, w.p.1, but for λ > 1/8 the number of particles in any open set grows to ∞ w.p.1. In the subcritical case (λ≦ 1/8) the set Λ of all limit points in ∂?2… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 11 REFERENCES
    The Contact Process on Trees
    136
    Geometry and Spectra of Compact Riemann Surfaces
    762
    Stochastic models of interacting systems
    69
    A conditional limit theorem for the frontier of a branching Brownian motion
    108
    E(j ? 0 j ?+3
      Geometry of Discrete Groups
      363
      Markov Chains Indexed by Trees
      158
      Random Walks and Percolation on Trees
      308
      The Inverse Gaussian Distribution
      73
      The Inverse Gaussian Distribution.
      147