Geodesic
Limit theorems for the number of clusters of the Arratia flow
Teoriâ slučajnyh processov, Tome 23 (2018) no. 2, pp. 33-40

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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. 
@article{THSP_2018_23_2_a3,
     author = {E. V. Glinyanaya and V. V. Fomichov},
     title = {Limit theorems for the number of clusters of the {Arratia} flow},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {33--40},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2018_23_2_a3/}
}
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E. V. Glinyanaya; V. V. Fomichov. Limit theorems for the number of clusters of the Arratia flow. Teoriâ slučajnyh processov, Tome 23 (2018) no. 2, pp. 33-40. http://geodesic.mathdoc.fr/item/THSP_2018_23_2_a3/