We study a natural generalization of the Λ-coalescent to a spatial continuum. We introduce the process, which is known as the Segregated Λ-coalescent, via its connections to the (non-spatial) Λ-coalescent and the Spatial Λ-Fleming-Viot process. The main new results contained in this thesis are as follows. The Segregated Λ-coalescent has a non-trivial construction which we present here in terms of stochastic flows. We describe the qualitative behaviour of the Segregated Λ-coalescent and compare it to the behaviour of the Λ-coalescent, showing in particular that the Segregated Λ-coalescent has an extra phase transition which is directly related to the introduction of space. We finish with some results concerning the rate at which the Segregated Λ-coalescent comes down from infinity.
Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:658383 |
Date | January 2012 |
Creators | Freeman, Nicholas |
Contributors | Hambly, Ben |
Publisher | University of Oxford |
Source Sets | Ethos UK |
Detected Language | English |
Type | Electronic Thesis or Dissertation |
Source | http://ora.ox.ac.uk/objects/uuid:fb162fbf-2fa2-40d7-af84-c6e3744e35c1 |
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