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 Theory Stoch. Process.: Year: Volume: Issue: Page: Find

 Theory Stoch. Process., 2012, Volume 18(34), Issue 2, Pages 1–7 (Mi thsp24)

Iterated logarithm law for sizes of clusters in Arratia flow

A. A. Dorogovtseva, A. V. Gnedinb, M. B. Vovchanskiia

a Institute of Mathematics of the NAS of Ukraine
b Queen Mary, University of London

Abstract: 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.

Keywords: Arratia flow, cluster, Brownian motion, Gaussian processes, concentration of measure.

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Bibliographic databases:
MSC: Primary 60J65; Secondary 60D05
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Citation: A. A. Dorogovtsev, A. V. Gnedin, M. B. Vovchanskii, “Iterated logarithm law for sizes of clusters in Arratia flow”, Theory Stoch. Process., 18(34):2 (2012), 1–7

Citation in format AMSBIB
\Bibitem{DorGneVov12} \by A.~A.~Dorogovtsev, A.~V.~Gnedin, M.~B.~Vovchanskii \paper Iterated logarithm law for sizes of clusters in Arratia flow \jour Theory Stoch. Process. \yr 2012 \vol 18(34) \issue 2 \pages 1--7 \mathnet{http://mi.mathnet.ru/thsp24} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3124769} \zmath{https://zbmath.org/?q=an:1289.60132}