[{"publication":"XIVth International Congress on Mathematical Physics","quality_controlled":"1","status":"public","publisher":"World Scientific","publication_status":"published","month":"03","extern":"1","date_published":"2006-03-01T00:00:00Z","_id":"8515","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"}],"date_created":"2020-09-18T10:48:59Z","page":"290-295","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:19:49Z","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9789812562012","9789812704016"]},"doi":"10.1142/9789812704016_0026","day":"01","author":[{"last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","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"}],"type":"conference","year":"2006","oa_version":"None","citation":{"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.","ieee":"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.","chicago":"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>.","mla":"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>.","short":"V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–295.","apa":"Kaloshin, V., DOLGOPYAT, D., &#38; 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>","ama":"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>"},"title":"Long time behaviour of periodic stochastic flows","conference":{"location":"Lisbon, Portugal","end_date":"2003-08-02","start_date":"2003-07-28","name":"International Congress on Mathematical Physics"}}]