%0 Journal Article %1 limic2006spatial %A Limic, Vlada %A Sturm, Anja %D 2006 %K coalescent_theory lambda_coalescent spatial_coalescent %T The spatial $Łambda$-coalescent %U http://ejp.ejpecp.org/article/view/319 %X 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.

@article{limic2006spatial, 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.}, added-at = {2015-06-15T03:14:07.000+0200}, author = {Limic, Vlada and Sturm, Anja}, biburl = {https://www.bibsonomy.org/bibtex/21b407fe168617d3e78b708a464289baa/peter.ralph}, id = {319, 363-393, 10.1214/EJP.v11-319, http://ejp.ejpecp.org/article/view/319}, interhash = {bac1a459c737975ca3f89aecb19489f3}, intrahash = {1b407fe168617d3e78b708a464289baa}, keywords = {coalescent_theory lambda_coalescent spatial_coalescent}, timestamp = {2015-06-15T03:14:07.000+0200}, title = {The spatial $\Lambda$-coalescent}, type = {Text.Serial.Journal}, url = {http://ejp.ejpecp.org/article/view/319}, year = 2006 }