Speed of coming down from infinity for Λ-Fleming-Viot initial support

Λ-Fleming-Viot process is a probability-measure-valued process that is dual to a Λ-coalescent involving
multiple collisions. It is well known that such a process can have the compact support property, i.e. its support
becomes finite at any positive time even though the initial measure has an unbounded support.
       For Λ-Fleming-Viot processes with Brownian spatial motion and with the associated Λ-coalescents coming down from infinity, applying the lookdown representation we obtain asymptotic results characterizing how fast the initial supports become finite. Our results are expressed using asymptotics of tail distributions of the initial measures and speed functions of coming down from infinity for the associated Λ-coalescents. We will also mention briefly the parallel results for super-Brownian motions.
        This talk is based on joint work with Zenghu Li and Huili Liu.