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Hausdorff dimension in stochastic dispersion

Dmitry Dolgopyat·Vadim Kaloshin·Leonid Koralov
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Abstract

We consider the evolution of a connected set in Euclidean space carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order sqrt{t} away from the origin [DKK1], there is an uncountable set of measure zero of points, which escape to infinity at the linear rate [CSS1]. In this paper we prove that this set of linear escape points has full Hausdorff dimension.

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Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov. 2002-05-03. Hausdorff dimension in stochastic dispersion. https://arxiv.org/abs/math/0205032

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