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

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.

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Vlada Limic. Anja Sturm. "The spatial $\Lambda$-coalescent." Electron. J. Probab. 11 363 - 393, 2006. https://doi.org/10.1214/EJP.v11-319

Information

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

Subjects:
Primary: 60J25
Secondary: 60K35

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