Remarks on hyperbolic branching Brownian motion

par Wolfgang Woess (TU Graz)

vendredi 17 avr. 2026, 13:30 → 14:30 Europe/Paris

E2 1180 (Tours)

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 dependence on the fission rate of the branching particles. In the talk, further features are exhibited. The rates of the maximal and minimal hyperbolic distances to the starting point are determined, as well as refined asymptotic estimates in the transient regime. The other main issues studied here concern the behaviour of the empiricial distributions of the branching  population, as time goes to infinity, and their convergence to   an infinitely supported random limit probability measure on the  boundary.

The talk concludes with some open questions hat I had posed and recent answers by D. Geldbach (Oxford).