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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- Department of Mathematical Sciences - Lecturer & Royal Society Research Fellow
- Probability Laboratory at Bath
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching, Researcher