Coming down from infinity for local-time coalescing Brownian motions

Coming down from infinity is a phenomenon where a Markov process, typically modeling population dynamics, begins with an infinitely large population that will collapse and become finite, almost surely, for any positive time. We give necessary and sufficient conditions describing when coming down from infinity holds for local-time coalescing Brownian motions.  Furthermore, we determine the rate in which the population decreases from infinity when coming down from infinity. Joint work with Leonid Mytnik and Zhen Yao Sun.