Iterated logarithm law for sizes of clusters in Arratia flow

A. A. Dorogovtsev, A. V. Gnedin, M. B. Vovchanskii
Theory of Stochastic Processes
Vol.18 (34), no.2, 2012, pp.1-7
The asymptotics of sizes of clusters for the Arratia flow is considered, the Arratia flow being a system of coalescing Wiener processes starting from the real axis and independent before they meet. A cluster at time $t$ is defined as a set of particles that have glued together not later than at $t.$ The results obtained are remarked to hold for any Arratia flow with a Lipschitz drift.