Hausdorff dimension in stochastic dispersion

2002/05/03 by Dmitry Dolgopyat, Vadim Kaloshin, Dolgopyat, Dmitry +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.math/0205032

26 pages

arxiv created 2002/05/03 · arxiv updated 2009/11/30

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 sqrtt 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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