Notes on hyperbolic branching Brownian motion

Euclidean branching Brownian motion (BBM) has been intensively studied during many decades by renowned researchers. BBM on hyperbolic space has received less attention. A profound study of Lalley and Sellke (1997) provided insight on the recurrent, resp. transient regimes of BBM on the Poincare' disk. In particular, they determined the Hausdorff dimension of the limit set on the boundary circle in dependance on the fission rate of the branching particles. In the present notes, some further features are exhibited, such as the rate of the maximal hyperbolic distance to the starting point and the behaviour of the empiricial distributions of the branching population, as time goes to infinity.