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

Alison Etheridge; Nic Freeman; Sarah Penington

doi:10.1214/17-EJP127

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

Alison Etheridge
, Nic Freeman
, Sarah Penington

Department of Mathematical Sciences

University of Oxford
University of Sheffield

Research output: Contribution to journal › Article › peer-review

14 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 language	English
Article number	103
Pages (from-to)	1-40
Number of pages	40
Journal	Electronic Journal of Probability
Volume	22
Early online date	7 Dec 2017
DOIs	https://doi.org/10.1214/17-EJP127
Publication status	Published - 31 Dec 2017

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10.1214/17-EJP127

https://arxiv.org/abs/1607.07563v1

Sarah Penington
- S.Peningtonbath.acuk
- Department of Mathematical Sciences - Royal Society Research Fellow (and Proleptic Reader)
- Probability Laboratory at Bath
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching, Core staff

Cite this

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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 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.",

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

Abstract

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Sarah Penington

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