A limit shape theorem for periodic stochastic dispersion

@article{Dolgopyat2002ALS,
  title={A limit shape theorem for periodic stochastic dispersion},
  author={Dmitry Dolgopyat and Vadim Kaloshin and Leonid Koralov},
  journal={Communications on Pure and Applied Mathematics},
  year={2002},
  volume={57}
}
We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t most of the particles are at a distance of order $\sqrt{t}$ away from the origin, there is a measure zero set of points that escape to infinity at the linear rate. We study the set of points visited by the original set by time t and show that such a set, when scaled down by the factor of t, has a limiting… 
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