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

摘要

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.