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

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