A limit shape theorem for periodic stochastic dispersion
Abstract
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 of the particles are at a distance of order sqrt{t} away from the origin, there is a measure zero set of points, which 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 non random shape.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2002
 DOI:
 10.48550/arXiv.math/0205033
 arXiv:
 arXiv:math/0205033
 Bibcode:
 2002math......5033D
 Keywords:

 Probability;
 Dynamical Systems
 EPrint:
 22 pages, 5 figures