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.
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