Branching Brownian motion, mean curvature flow and the motion of hybrid zones
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 wha...
| Κύριοι συγγραφείς: | , , |
|---|---|
| Μορφή: | Journal article |
| Έκδοση: |
Institute of Mathematical Statistics
2017
|
| Περίληψη: | 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. |
|---|