Hausdorff dimension in stochastic dispersion
Probability
2007-05-23 v1 Dynamical Systems
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.
Cite
@article{arxiv.math/0205032,
title = {Hausdorff dimension in stochastic dispersion},
author = {Dmitry Dolgopyat and Vadim Kaloshin and Leonid Koralov},
journal= {arXiv preprint arXiv:math/0205032},
year = {2007}
}
Comments
26 pages