We consider the long-time behaviour of a “heterogeneous” binary branching Brownian motion (BBM), in which the branching rate depends on the location of the diffusing particle. More precisely, for a nonnegative function g, the instantaneous branching rate of a particle at location x is characterized by g(x) (we refer to this as g-BBM). When g is periodic, we expect that the microscopic effects of g average out on large scales, and the process should exhibit asymptotically homogeneous behaviour. Nevertheless, the heterogeneity of the branching rate introduces new technical challenges.

In this talk, I will present a shape theorem for the convex hull of a periodic g-BBM in all dimensions. This talk is based  on joint work with Louigi Addario-Berry (McGill) and Arturo Arellano Arias (McGill).

Speaker: Jessica Lin, McGill