Journal article

Branching Brownian motion, mean curvature flow and the motion of hybrid zones

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.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Etheridge, A., Freeman, N., & Penington, S. (2017). Branching Brownian motion, mean curvature flow and the motion of hybrid zones. Electronic Journal of Probability, 22.

MLA Style

Etheridge, A, et al. “Branching Brownian Motion, Mean Curvature Flow and the Motion of Hybrid Zones.” Electronic Journal of Probability, vol. 22, 2017.

Chicago Style

Etheridge, A, N Freeman, and S Penington. 2017. “Branching Brownian Motion, Mean Curvature Flow and the Motion of Hybrid Zones.” Electronic Journal of Probability 22.
Print

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Files:: euclid.ejp.1512615692.pdf

(Preview, Version of record, pdf, 466.1KB, Terms of use)

Publisher copy:: 10.1214/17-EJP127

Authors

+ Etheridge, A More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: Magdalen College
Role:: Author

+ Freeman, N More by this author

Role:: Author

+ Penington, S More by this author

Institution:: University of Oxford
Division:: MPLS Division
Department:: Statistics; Mathematical Institute
Role:: Author

Publisher:: Institute of Mathematical Statistics
Journal:: Electronic Journal of Probability More from this journal
Volume:: 22
Article number:: 103
Publication date:: 2017-12-07
Acceptance date:: 2017-11-17
DOI:: 10.1214/17-EJP127
ISSN:: 1083-6489

Keywords:: spatial Λ-Fleming-Viot

Branching Brownian motion

hybrid zones

population genetics

mean curvature flow
Pubs id:: pubs:797451
UUID:: uuid:5955939b-8cf5-4cc7-94be-a80d094531a6
Local pid:: pubs:797451
Source identifiers:: 797451
Deposit date:: 2017-11-27
ARK identifier:: ark:/29072/ora_5955939b8cf54cc794bea80d094531a6

Terms of use

Copyright holder:: Etheridge et al
Copyright date:: 2017
Notes:: This article has been made available under a Creative Commons Attribution 4.0 International License.

Licence:: CC Attribution (CC BY)

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