The Segregated Lambda-coalescent

Nic P Freeman

Research output: Other contribution


We construct an extension of the Lambda-coalescent to a spatial continuum and analyse its behaviour. Like the Lambda-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 Lambda-coalescent theory and directly reflect the incorporation of space into our model. Firstly, our semicritical phase sees a null but non-empty 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.
Original languageEnglish
Media of outputPDF, text
Number of pages36
Publication statusPublished - 20 Sep 2011

Bibliographical note

Updated to accepted article - to appear in the Annals of Probability. 36 pages, 2 figures


  • math.PR
  • 60J25 60J85 92D25


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