# A limit shape theorem for periodic stochastic dispersion

Dolgopyat D, Kaloshin V, Koralov L. 2004. A limit shape theorem for periodic stochastic dispersion. Communications on Pure and Applied Mathematics. 57(9), 1127–1158.

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*Journal Article*|

*Published*|

*English*

Author

Dolgopyat, Dmitry;
Kaloshin, Vadim

^{ISTA}^{}; Koralov, LeonidAbstract

We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t most of the particles are at a distance of order equation image away from the origin, there is a measure zero set of points that 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 nonrandom shape.

Keywords

Publishing Year

Date Published

2004-09-01

Journal Title

Communications on Pure and Applied Mathematics

Volume

57

Issue

9

Page

1127-1158

IST-REx-ID

### Cite this

Dolgopyat D, Kaloshin V, Koralov L. A limit shape theorem for periodic stochastic dispersion.

*Communications on Pure and Applied Mathematics*. 2004;57(9):1127-1158. doi:10.1002/cpa.20032Dolgopyat, D., Kaloshin, V., & Koralov, L. (2004). A limit shape theorem for periodic stochastic dispersion.

*Communications on Pure and Applied Mathematics*. Wiley. https://doi.org/10.1002/cpa.20032Dolgopyat, Dmitry, Vadim Kaloshin, and Leonid Koralov. “A Limit Shape Theorem for Periodic Stochastic Dispersion.”

*Communications on Pure and Applied Mathematics*. Wiley, 2004. https://doi.org/10.1002/cpa.20032.D. Dolgopyat, V. Kaloshin, and L. Koralov, “A limit shape theorem for periodic stochastic dispersion,”

*Communications on Pure and Applied Mathematics*, vol. 57, no. 9. Wiley, pp. 1127–1158, 2004.Dolgopyat, Dmitry, et al. “A Limit Shape Theorem for Periodic Stochastic Dispersion.”

*Communications on Pure and Applied Mathematics*, vol. 57, no. 9, Wiley, 2004, pp. 1127–58, doi:10.1002/cpa.20032.