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

Alison Etheridge, Nic Freeman, Sarah Penington

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)

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 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.
Original languageEnglish
Article number103
Pages (from-to)1-40
Number of pages40
JournalElectronic Journal of Probability
Volume22
Early online date7 Dec 2017
DOIs
Publication statusPublished - 31 Dec 2017

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