Open Access
2006 The spatial $\Lambda$-coalescent
Vlada Limic, Anja Sturm
Author Affiliations +
Electron. J. Probab. 11: 363-393 (2006). DOI: 10.1214/EJP.v11-319


This paper extends the notion of the $\Lambda$-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial $\Lambda$-coalescent migrate in a (finite) geographical space and may only coalesce if located at the same site of the space. We characterize the $\Lambda$-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 $\Lambda$-coalescents on large tori in $d\geq 3$ dimensions. Some of our results generalize and strengthen the corresponding results in Greven et al. (2005) concerning the spatial Kingman coalescent.


Download Citation

Vlada Limic. Anja Sturm. "The spatial $\Lambda$-coalescent." Electron. J. Probab. 11 363 - 393, 2006.


Accepted: 19 May 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1113.60077
MathSciNet: MR2223040
Digital Object Identifier: 10.1214/EJP.v11-319

Primary: 60J25
Secondary: 60K35

Keywords: $la$-coalescent , Coalescent , Coalescing random walks , limit theorems , structured coalescent

Vol.11 • 2006
Back to Top