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Publication 09-CNA-16
Exit Times of Diffusions with Incompressible Drift Gautam Iyer
Carnegie Mellon University Department of Mathematical Sciences Pittsburgh, PA 15213 gi1242@andrew.cmu.edu lexei Novikov Lenya Ryzhik Andrej Zlatos Abstract: Let be a bounded domain and for let be the expected exit time from of a diffusing particle starting at and advected by an incompressible flow . We are interested in the question which flows maximize , that is, they are most efficient in the creation of hotspots inside . Surprisingly, among all simply connected domains in two dimensions, the discs are the only ones for which the zero flow maximises . We also show that in any dimension, among all domains with a fixed volume and all incompressible flows on them, is maximized by the zero flow on the ball. Get the paper in its entirety as |