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