@article{EJP319,
author = {Vlada Limic and Anja Sturm},
title = {The spatial $\Lambda$-coalescent},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {coalescent; \$la\$-coalescent; structured coalescent; limit theorems, coalescing random walks},
abstract = {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.},
pages = {no. 15, 363-393},
issn = {1083-6489},
doi = {10.1214/EJP.v11-319},
url = {http://ejp.ejpecp.org/article/view/319}}