The spatial $\Lambda$-coalescent
The spatial $\Lambda$-coalescent
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空间$Lambda$-聚结
DOI：
10.1214/ejp.v11-319
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发表时间：
2005
影响因子：
1.4
通讯作者：
A. Sturm
中科院分区：
文献类型：
--
作者：
V. Limic;A. Sturm
本文将皮特曼（1999）的$\Lambda$-聚结的概念推广到空间环境。空间$\Lambda$-聚结的分区元素在（有限的）地理空间中迁移，并且只有位于空间的同一地点时才可能聚结。我们以类似于Schweinsberg（2000）的方式描述了从无穷大下降的$\Lambda$-聚结子。令人惊讶的是，所有从无限下降的空间聚合物，也以统一的方式从无限下降。这使我们能够研究空间$\Lambda$-聚结大环面在$d\geq 3$维的时空渐近性。我们的一些结果推广和加强了Greven等人（2005）关于空间金曼聚结的相应结果。
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.