A limit shape theorem for periodic stochastic dispersion
Probability
2007-05-23 v1 Dynamical Systems
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.
Cite
@article{arxiv.math/0205033,
title = {A limit shape theorem for periodic stochastic dispersion},
author = {Dmitry Dolgopyat and Vadim Kaloshin and Leonid Koralov},
journal= {arXiv preprint arXiv:math/0205033},
year = {2007}
}
Comments
22 pages, 5 figures