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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.
Citation:
E. V. Glinyanaya, V. V. Fomichov, “Limit theorems for the number of clusters of the Arratia flow”, Theory Stoch. Process., 23(39):2 (2018), 33–40
Linking options:
https://www.mathnet.ru/eng/thsp292 https://www.mathnet.ru/eng/thsp/v23/i2/p33
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