Long time behaviour of periodic stochastic flows

V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–295.

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Conference Paper | Published | English
Author
Kaloshin, VadimIST Austria; DOLGOPYAT, D.; KORALOV, L.
Abstract
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.
Publishing Year
Date Published
2006-03-01
Proceedings Title
XIVth International Congress on Mathematical Physics
Page
290-295
Conference
International Congress on Mathematical Physics
Conference Location
Lisbon, Portugal
Conference Date
2003-07-28 – 2003-08-02
IST-REx-ID

Cite this

Kaloshin V, DOLGOPYAT D, KORALOV L. Long time behaviour of periodic stochastic flows. In: XIVth International Congress on Mathematical Physics. World Scientific; 2006:290-295. doi:10.1142/9789812704016_0026
Kaloshin, V., DOLGOPYAT, D., & KORALOV, L. (2006). Long time behaviour of periodic stochastic flows. In XIVth International Congress on Mathematical Physics (pp. 290–295). Lisbon, Portugal: World Scientific. https://doi.org/10.1142/9789812704016_0026
Kaloshin, Vadim, D. DOLGOPYAT, and L. KORALOV. “Long Time Behaviour of Periodic Stochastic Flows.” In XIVth International Congress on Mathematical Physics, 290–95. World Scientific, 2006. https://doi.org/10.1142/9789812704016_0026.
V. Kaloshin, D. DOLGOPYAT, and L. KORALOV, “Long time behaviour of periodic stochastic flows,” in XIVth International Congress on Mathematical Physics, Lisbon, Portugal, 2006, pp. 290–295.
Kaloshin V, DOLGOPYAT D, KORALOV L. 2006. Long time behaviour of periodic stochastic flows. XIVth International Congress on Mathematical Physics. International Congress on Mathematical Physics 290–295.
Kaloshin, Vadim, et al. “Long Time Behaviour of Periodic Stochastic Flows.” XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–95, doi:10.1142/9789812704016_0026.

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