@inproceedings{8515,
  abstract     = {We consider the evolution of a set carried by a space periodic incompressible stochastic flow in a Euclidean space. We
report on three main results obtained in [8, 9, 10] concerning long time behaviour for a typical realization of the stochastic flow. First, at time t most of the particles are at a distance of order √t away from the origin. Moreover, we prove a Central Limit Theorem for the evolution of a measure carried by the flow, which holds for almost every realization of the flow. Second, we show the existence of a zero measure full Hausdorff dimension set of points, which
escape to infinity at a linear rate. Third, in the 2-dimensional case, we study the set of points visited by the original set by time t. Such a set, when scaled down by the factor of t, has a limiting non random shape.},
  author       = {Kaloshin, Vadim and DOLGOPYAT, D. and KORALOV, L.},
  booktitle    = {XIVth International Congress on Mathematical Physics},
  isbn         = {9789812562012},
  location     = {Lisbon, Portugal},
  pages        = {290--295},
  publisher    = {World Scientific},
  title        = {{Long time behaviour of periodic stochastic flows}},
  doi          = {10.1142/9789812704016_0026},
  year         = {2006},
}