The segregated lambda-coalescent - Freeman, N (2012)
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.