--- _id: '8515' abstract: - lang: eng text: "We consider the evolution of a set carried by a space periodic incompressible stochastic flow in a Euclidean space. We\r\nreport 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\r\nescape 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." article_processing_charge: No author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: D. full_name: DOLGOPYAT, D. last_name: DOLGOPYAT - first_name: L. full_name: KORALOV, L. last_name: KORALOV citation: ama: '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' apa: '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' chicago: 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. ieee: 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. ista: 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. mla: 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. short: V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–295. conference: end_date: 2003-08-02 location: Lisbon, Portugal name: International Congress on Mathematical Physics start_date: 2003-07-28 date_created: 2020-09-18T10:48:59Z date_published: 2006-03-01T00:00:00Z date_updated: 2021-01-12T08:19:49Z day: '01' doi: 10.1142/9789812704016_0026 extern: '1' language: - iso: eng month: '03' oa_version: None page: 290-295 publication: XIVth International Congress on Mathematical Physics publication_identifier: isbn: - '9789812562012' - '9789812704016' publication_status: published publisher: World Scientific quality_controlled: '1' status: public title: Long time behaviour of periodic stochastic flows type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2006' ...