Etheridge, A., Freeman, N.P. and Penington, S. (2017) Branching Brownian Motion, mean curvature flow and the motion of hybrid zones. Electronic Journal of Probability, 22 (103). pp. 1-40. ISSN 1083-6489
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Institute of Mathematical Statistics. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Nov 2016 15:15 |
Last Modified: | 27 Jan 2020 14:47 |
Published Version: | https://doi.org/10.1214/17-EJP127 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/17-EJP127 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:105934 |