Electronic Journal of Probability

The spatial $\Lambda$-coalescent

Vlada Limic and Anja Sturm

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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.

Article information

Electron. J. Probab., Volume 11 (2006), paper no. 15, 363-393.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

coalescent $la$-coalescent structured coalescent limit theorems coalescing random walks

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Limic, Vlada; Sturm, Anja. The spatial $\Lambda$-coalescent. Electron. J. Probab. 11 (2006), paper no. 15, 363--393. doi:10.1214/EJP.v11-319. https://projecteuclid.org/euclid.ejp/1464730550

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