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 Electronic Journal of Probability > Vol. 11 (2006) > Paper 15 open journal systems 


The spatial Λ-coalescent

Vlada Limic, University of British Columbia
Anja Sturm, University of Delaware


Abstract
This paper extends the notion of the Λ-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial Λ-coalescent migrate in a (finite) geographical space and may only coalesce if located at the same site of the space. We characterize the Λ-coalescents that come down from infinity, in an analogous way to Schweinsberg (2000). Surprisingly, all spatial coalescents that come down from infinity, also come down from infinity in a uniform way. This enables us to study space-time asymptotics of spatial Λ-coalescents on large tori in d ≥ 3 dimensions. Some of our results generalize and strengthen the corresponding results in Greven et al.~(2005) concerning the spatial Kingman coalescent.


Full text: PDF

Pages: 363-393

Published on: May 19, 2006


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