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Applied
Math Seminar |
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We consider a problem of transport in random media or a problem evolution of an oil spot $B$ (a passive scalar or simply a shaded ball) on a surface of ocean (2-dim'l plane) under a random flow. If a random flow has no drift than a typical point of a flow at time t is at distance of order $\sqrt{t}$. However as M. Cranston, M. Schuetzow, D. Steinsaltz showed the diameter of an oil spot $B_t$ growth linearly in time $t$. We discuss various results related to this problem: CLT's for multipoint motion and measures, Shape theorem, and calculate the value of Hausdorff dimension of points in the oil spot $B$ escaping to infinity with linear speed in time. This is a joint work with D.Dolgopiat and L.Koralov |