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 | |
| Publication status | Published - 31 Dec 2017 |
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Dive into the research topics of 'Branching Brownian motion, mean curvature flow and the motion of hybrid zones'. Together they form a unique fingerprint.Profiles
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Sarah Penington
- 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, Researcher