## Electronic Journal of Probability

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

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 103, 40 pp.

Dates
Accepted: 17 November 2017
First available in Project Euclid: 7 December 2017

https://projecteuclid.org/euclid.ejp/1512615692

Digital Object Identifier
doi:10.1214/17-EJP127

Mathematical Reviews number (MathSciNet)
MR3733661

Zentralblatt MATH identifier
06827080

#### Citation

Etheridge, Alison; Freeman, Nic; Penington, Sarah. Branching Brownian motion, mean curvature flow and the motion of hybrid zones. Electron. J. Probab. 22 (2017), paper no. 103, 40 pp. doi:10.1214/17-EJP127. https://projecteuclid.org/euclid.ejp/1512615692

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