Branching Brownian motion, mean curvature flow and the motion of hybrid zones
Copyright policy )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 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.
41 pages
Probability (math.PR), population genetics, branching Brownian motion, spatial $\Lambda $-Fleming-Viot, 92D15, mean curvature flow, hybrid zones, 60J70, 60J85, 92D15, Problems related to evolution, spatial \(\Lambda\)-Fleming-Viot, Applications of branching processes, FOS: Mathematics, 60J85, Mathematics - Probability
Probability (math.PR), population genetics, branching Brownian motion, spatial $\Lambda $-Fleming-Viot, 92D15, mean curvature flow, hybrid zones, 60J70, 60J85, 92D15, Problems related to evolution, spatial \(\Lambda\)-Fleming-Viot, Applications of branching processes, FOS: Mathematics, 60J85, Mathematics - Probability
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