Abstract
The totally disconnectedness of support for super Brownian motion in high dimensions is well known. In this paper, we prove that similar results also hold for $\Lambda$-Fleming-Viot process with Brownian spatial motion provided that the associated $\Lambda$-coalescent does not come down from infinity fast enough. Our proof is another application of the lookdown particle representation for $\Lambda$-Fleming-Viot process. We also discuss the disjointness of independent $\Lambda$-Fleming-Viot supports and ranges in high dimensions. The disconnectedness of the $\Lambda$-Fleming-Viot support remains open in certain low dimensions.
Citation
Xiaowen Zhou. "On criteria of disconnectedness of $\Lambda$-Fleming-Viot support." Electron. Commun. Probab. 19 1 - 16, 2014. https://doi.org/10.1214/ECP.v19-3208
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