Electronic Journal of Probability

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

Alison Etheridge, Nic Freeman, and Sarah Penington

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1512615692

Digital Object Identifier
doi:10.1214/17-EJP127

Mathematical Reviews number (MathSciNet)
MR3733661

Zentralblatt MATH identifier
06827080

Subjects
Primary: 60J85: Applications of branching processes [See also 92Dxx] 92D15: Problems related to evolution

Keywords
branching Brownian motion mean curvature flow hybrid zones spatial $\Lambda $-Fleming-Viot population genetics

Rights
Creative Commons Attribution 4.0 International License.

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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