Branching Brownian Motion, mean curvature flow and the motion of hybrid zones

Alison Etheridge; Nic Freeman; Sarah Penington

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arXiv · 1607.07563

Branching Brownian Motion, mean curvature flow and the motion of hybrid zones

Alison Etheridge·Nic Freeman·Sarah Penington

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Abstract

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 $\Lambda$-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.

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Alison Etheridge, Nic Freeman, Sarah Penington. 2016-07-26. Branching Brownian Motion, mean curvature flow and the motion of hybrid zones. https://arxiv.org/abs/1607.07563

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