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