Anja Sturm
University of Delaware
Title: Spatial coalescent processes with multiple collisions.
This talk extends the Lambda-coalescent of Pitman (1999), also called the coalescent with multiple collisions, to a spatial setting. The non-spatial Lambda-coalescent is a Markov process whose state space is the set of partitions of the positive integers. The measure Lambda dictates the rate of coalescence events, as well as how many of the (exchangeable) partitions may coalesce (or merge) into one at any such event. The partition elements of the spatial Lambda-coalescent migrate in a geographical space and may only coalesce (according to a non-spatial Lambda-coalescent) if located at the same site of the space. We characterize the spatial Lambda-coalescents that come down from infinity, which means that started from infinitely many partitions the process coalesces to a finite number of partitions immediately. Surprisingly, all spatial Lambda-coalescents that come down from infinity, also come down from infinity in a uniform way. This makes it possible to study space-time asymptotics of these colaescents on large finite tori in at least three dimensions at time scales on the order of the torus volume. The limit process for the partitions is identified as a (non-spatial) Kingman coalescent started from an entrance law that depends on the initial configuration as well as on the underlying Lambda-coalescent.

This is joint work with Vlada Limic (University of British Columbia).
©2005, Department of Mathematical Sciences
Last Modified: August 26, 2005