%0 Generic %1 etheridge2016branching %A Etheridge, Alison %A Freeman, Nic %A Penington, Sarah %D 2016 %K SLFV branching_Brownian_motion curvature_flow duality hybrid_zone spatial_branching %T Branching Brownian Motion, mean curvature flow and the motion of hybrid zones %U http://arxiv.org/abs/1607.07563 %X 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 $Łambda$-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.

@misc{etheridge2016branching, 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 $\Lambda$-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.}, added-at = {2016-08-18T17:50:18.000+0200}, author = {Etheridge, Alison and Freeman, Nic and Penington, Sarah}, biburl = {https://www.bibsonomy.org/bibtex/2b40a70c2a0bdb82b6e836f5722d0b843/peter.ralph}, interhash = {6f5b4755467148f83a1e82fff4213281}, intrahash = {b40a70c2a0bdb82b6e836f5722d0b843}, keywords = {SLFV branching_Brownian_motion curvature_flow duality hybrid_zone spatial_branching}, note = {cite arxiv:1607.07563}, timestamp = {2016-08-18T17:50:18.000+0200}, title = {Branching {Brownian} Motion, mean curvature flow and the motion of hybrid zones}, url = {http://arxiv.org/abs/1607.07563}, year = 2016 }