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2017 Branching Brownian motion, mean curvature flow and the motion of hybrid zones
Alison Etheridge, Nic Freeman, Sarah Penington
Electron. J. Probab. 22: 1-40 (2017). DOI: 10.1214/17-EJP127


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. "Branching Brownian motion, mean curvature flow and the motion of hybrid zones." Electron. J. Probab. 22 1 - 40, 2017.


Received: 7 July 2017; Accepted: 17 November 2017; Published: 2017
First available in Project Euclid: 7 December 2017

zbMATH: 06827080
MathSciNet: MR3733661
Digital Object Identifier: 10.1214/17-EJP127

Primary: 60J85 , 92D15

Keywords: Branching Brownian motion , hybrid zones , Mean curvature flow , Population genetics , spatial $\Lambda $-Fleming-Viot


Vol.22 • 2017
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