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JOURNALS // Theory of Stochastic Processes // Archive

Theory Stoch. Process., 2018 Volume 23(39), Issue 2, Pages 33–40 (Mi thsp292)

Limit theorems for the number of clusters of the Arratia flow

E. V. Glinyanaya, V. V. Fomichov

Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska str. 3, Kiev 01004, Ukraine

Abstract: 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 $n\to\infty$, obtain an estimate of the Berry–Esseen type for the rate of this convergence, and prove the corresponding functional law of the iterated logarithm.

Keywords: Central limit theorem, Berry–Esseen inequality, functional law of the iterated logarithm, coalescing Brownian motions, Arratia flow, clusters.

MSC: Primary 60F05, 60F17, 60G55; Secondary 60G60

Language: English



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