Hyperbolic branching Brownian motion
نویسندگان
چکیده
Hyperbolic branching Brownian motion is a branching di usion process in which individual particles follow independent Brownian paths in the hyperbolic plane H2, and undergo binary ssion(s) at rate ¿0. It is shown that there is a phase transition in : For 51=8 the number of particles in any compact region of H2 is eventually 0, w.p.1, but for ¿1=8 the number of particles in any open set grows to ∞ w.p.1. In the subcritical case ( 51=8) the set of all limit points in @H2 (the boundary circle at ∞) of particle trails is a Cantor set, while in the supercritical case ( ¿1=8) the set has full Lebesgue measure. For 51=8 it is shown that w.p.1 the Hausdor dimension of is =(1−√1− 8 )=2.
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