Electronic Journal of Probability

The spatial $\Lambda$-coalescent

Vlada Limic and Anja Sturm

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464730550

Digital Object Identifier
doi:10.1214/EJP.v11-319

Mathematical Reviews number (MathSciNet)
MR2223040

Zentralblatt MATH identifier
1113.60077

Subjects
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]

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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