Freeman, N.P. (2015) The Segregated Lambda-Coalescent. The Annals of Probability, 43 (2). pp. 435-467. ISSN 0091-1798
Abstract
We construct an extension of the ΛΛ-coalescent to a spatial continuum and analyse its behaviour. Like the ΛΛ-coalescent, the individuals in our model can be separated into (i) a dust component and (ii) large blocks of coalesced individuals. We identify a five phase system, where our phases are defined according to changes in the qualitative behaviour of the dust and large blocks. We completely classify the phase behaviour, including necessary and sufficient conditions for the model to come down from infinity.
We believe that two of our phases are new to ΛΛ-coalescent theory and directly reflect the incorporation of space into our model. Firstly, our semicritical phase sees a null but nonempty set of dust. In this phase the dust becomes a random fractal, of a type which is closely related to iterated function systems. Secondly, our model has a critical phase in which the coalescent comes down from infinity gradually during a bounded, deterministic time interval.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 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: | 22 Apr 2016 13:37 |
Last Modified: | 22 Apr 2016 13:37 |
Published Version: | https://dx.doi.org/10.1214/13-AOP857 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/13-AOP857 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98790 |