2005/11/22 by Vlada Limic, Limic, Vlada, Anja Sturm +1 · 1 citation
Computer Science · Mathematics · #60J25 #60K35 #Computational Geometry and Mesh Generation #Constraint Satisfaction and Optimization #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J25 #msc:60K35
paper · pdf · doi:10.48550/arxiv.math/0511536
29 pages
arxiv created 2005/11/22 · openalex publication_date 2005/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper extends the notion of the \la-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial Λ-coalescent migrate in a (finite) geographical space and may only coalesce if located at the same site of the space. We characterize the Λ-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 Λ-coalescents on large tori in d≥ 3 dimensions. Our results generalize and strengthen those of Greven et al. (2005), who studied the spatial Kingman coalescent in this context.