Abstract
This paper extends the notion of the $Łambda$-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial $Łambda$-coalescent migrate in a (finite) geographical space and may only coalesce if located at the same site of the space. We characterize the $Łambda$-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 $Łambda$-coalescents on large tori in $d3$ dimensions. Some of our results generalize and strengthen the corresponding results in Greven et al. (2005) concerning the spatial Kingman coalescent.
Users
Please
log in to take part in the discussion (add own reviews or comments).