Limit theorems for the number of clusters of the Arratia flow

E. V. Glinyanaya, V. V. Fomichov
Theory of Stochastic Processes
Vol.23 (39), no.2, 2018, pp.33-40
In this paper we prove the central limit theorem for the number of clusters formed by the particles of the Arratia flow starting from the interval [0;n] as n→∞, obtain an estimate of the Berry-Esseen type for the rate of this convergence, and prove the corresponding functional law of the iterated logarithm.