The compact support property for the $Λ$-Fleming-Viot process with underlying Brownian motion

Using the lookdown construction of Donnelly and Kurtz we prove that, at any fixed positive time, the $Λ$-Fleming-Viot process with underlying Brownian motion has a compact support provided that the corresponding $Λ$-coalescent comes down from infinity not too slowly. We also find both upper bound and lower bound on the Hausdorff dimension for the support.

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