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The spatial $\Lambda$-coalescent


 
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1. Title Title of document The spatial $\Lambda$-coalescent
 
2. Creator Author's name, affiliation, country Vlada Limic; University of British Columbia
 
2. Creator Author's name, affiliation, country Anja Sturm; University of Delaware
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) coalescent; $la$-coalescent; structured coalescent; limit theorems, coalescing random walks
 
3. Subject Subject classification 60J25; 60K35
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSERC
 
7. Date (YYYY-MM-DD) 2006-05-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/319
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-319
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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