University of California, Irvine, Mathematics

Michael Cranston, Professor

Department of Mathematics
University of California, Irvine
Irvine, CA 92697-3875

Office: MSTB 281
Phone: (949) 824-5507
Fax: (949) 824-7993
E-mail: mcransto@math.uci.edu

Research Area

My recent work has been on problems in three areas of probability theory. The first area is stochastic flows. The main problems I've studied here are on the dispersion of pollutants under turbulent and diffusive flow. A preprint on this subject is available below and here's a link to another in the Vol. 4, 1999 issue of ECP . The second area is on the parabolic Anderson problem. In joint work with Tom Mountford and Tokuzo Shiga on this subject we get existence of the Lyapunov exponent and its asymptotic behavior as diffusivity tends to zero. With Mountford, we've also considered the parablolic Anderson model in continuous space setting and derived the existence of the a.s. Lyapunov exponent. With Molchaonv, we're investigating various random media questions including some recent investigations into polymers. The third area is on random surface growth in collaboration with Yonathan Shapir (Physics, University of Rochester.) We're interested in scaling properties of the distribution of the maximal height of random surfaces. A recent reprint on this subject is available from Physics Review Letters,Vol. 87, Issue 13. Also check out these links for expository accounts of this work in the Science Daily and in the May/June issue of Erosion Control.


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