Iterated logarithm law for sizes of clusters in Arratia flow

A. A. Dorogovtsev; A. V. Gnedin; M. B. Vovchanskii

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arXiv · 1310.6692

Iterated logarithm law for sizes of clusters in Arratia flow

A. A. Dorogovtsev·A. V. Gnedin·M. B. Vovchanskii

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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.

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A. A. Dorogovtsev, A. V. Gnedin, M. B. Vovchanskii. 2013-10-24. Iterated logarithm law for sizes of clusters in Arratia flow. https://arxiv.org/abs/1310.6692

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