On criteria of disconnectedness of $\Lambda$-Fleming-Viot support

Xiaowen Zhou (Concordia University)

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.

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Pages: 1-16

Publication Date: August 11, 2014

DOI: 10.1214/ECP.v19-3208

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