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A limit shape theorem for periodic stochastic dispersion
Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov
We consider the evolution of a connected set on the plane carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most…
Hausdorff dimension in stochastic dispersion
Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov
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…
Sample path properties of the stochastic flows
Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov
We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as th…