涩里番

Title: A shape theorem for the d-dimensional branching Brownian motion in periodic environments.

Abstract: We consider the long-time behaviour of a "heterogeneous" binary branching Brownian motion (BBM) in which the branching rate depends on where the branching event occurs. More precisely, for a positive 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 prove a shape theorem for the convex hull of the g-BBM in all dimensions, namely that there exists a deterministic set W such that almost surely as t鈫掆垶, the g-BBM approximates tW. This talk is based on joint work with Louigi Addario-Berry (涩里番) and Jessica Lin (涩里番).

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