Branching Brownian motion, mean curvature flow and the motion of hybrid zones - Etheridge, A; Freeman, N; Penington, S (Institute of Mathematical Statistics, 2017)
We provide a probabilistic proof of a well known connection between a special case of the Allen-Cahn equation and mean curvature flow. We then prove a corresponding result for scaling limits of the spatial Λ-Fleming-Viot process with selection, in which the selection mechanism is chosen to model what are known in population genetics as hybrid zones. Our proofs will exploit a duality with a system of branching (and coalescing) random walkers which is of some interest in its own right.