conference paper
Long time behaviour of periodic stochastic flows
published
yes
Vadim
Kaloshin
author FE553552-CDE8-11E9-B324-C0EBE56974250000-0002-6051-2628
D.
DOLGOPYAT
author
L.
KORALOV
author
International Congress on Mathematical Physics
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.
World Scientific2006Lisbon, Portugal
eng
XIVth International Congress on Mathematical Physics
9789812562012
978981270401610.1142/9789812704016_0026
290-295
yes
V. Kaloshin, D. DOLGOPYAT, and L. KORALOV, “Long time behaviour of periodic stochastic flows,” in <i>XIVth International Congress on Mathematical Physics</i>, Lisbon, Portugal, 2006, pp. 290–295.
Kaloshin, Vadim, D. DOLGOPYAT, and L. KORALOV. “Long Time Behaviour of Periodic Stochastic Flows.” In <i>XIVth International Congress on Mathematical Physics</i>, 290–95. World Scientific, 2006. <a href="https://doi.org/10.1142/9789812704016_0026">https://doi.org/10.1142/9789812704016_0026</a>.
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.” <i>XIVth International Congress on Mathematical Physics</i>, World Scientific, 2006, pp. 290–95, doi:<a href="https://doi.org/10.1142/9789812704016_0026">10.1142/9789812704016_0026</a>.
Kaloshin V, DOLGOPYAT D, KORALOV L. Long time behaviour of periodic stochastic flows. In: <i>XIVth International Congress on Mathematical Physics</i>. World Scientific; 2006:290-295. doi:<a href="https://doi.org/10.1142/9789812704016_0026">10.1142/9789812704016_0026</a>
Kaloshin, V., DOLGOPYAT, D., & KORALOV, L. (2006). Long time behaviour of periodic stochastic flows. In <i>XIVth International Congress on Mathematical Physics</i> (pp. 290–295). Lisbon, Portugal: World Scientific. <a href="https://doi.org/10.1142/9789812704016_0026">https://doi.org/10.1142/9789812704016_0026</a>
V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–295.
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