Long time behaviour of periodic stochastic flows
Kaloshin, Vadim
DOLGOPYAT, D.
KORALOV, L.
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.
World Scientific
2006
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http://purl.org/coar/resource_type/c_5794
https://research-explorer.app.ist.ac.at/record/8515
Kaloshin V, DOLGOPYAT D, KORALOV L. Long time behaviour of periodic stochastic flows. In: <i>XIVth International Congress on Mathematical Physics</i>. World Scientific; 2006:290-295. doi:<a href="https://doi.org/10.1142/9789812704016_0026">10.1142/9789812704016_0026</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1142/9789812704016_0026
info:eu-repo/semantics/altIdentifier/isbn/9789812562012
info:eu-repo/semantics/altIdentifier/isbn/9789812704016
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