Hausdorff dimension in stochastic dispersion

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 `t away from the origin, (1) there is an uncountable set of measure zero of points, which escape to infinity at the linear rate. (2) In this paper we prove that this set of linear escape points has full Hausdorff dimension