Professor Ofer Zeitouni
will speak on
"Motion in random environment: conjectures, counter examples, and
“obvious" theorems"
The model of random walks in random environments generates several simple to formulate conjectures that are notoriously hard to resolve. I will describe the model and some of these conjectures. While those are undoubtedly true, I will present a couple of examples where counter-intuitive behavior occurs. I will then show, for the related model of diffusion in random environment with weak disorder, that homogenization does occur. In PDE terms, this amounts to showing the “obvious" result that, for dimension 3 or larger, solutions of the PDE $$ u_t = a_{ij}(x/\epsilon,\omega) u_{x_i,x_j} + b_i(x/\epsilon,\omega) u_{x_i}/\epsilon + g $$ with diffusion a and drift b that are small ergodic perturbations of the identity and of zero, respectively, and satisfy a statistical isotropy condition, converge uniformly on compacts to solutions of the heat equation $$ u_t = \sigma^2\Delta (u)+g . $$
Professor Yongbin Ruan, University of Wisconsin - Madison, will
visit the department for one month beginning October 3, 2004. His visit is
made possible by the Ordway Endowment. During his visit Professor Ruan's
office will be Vincent Hall 512; you can reach him by phone at 626-
9137.
Professor Louis Billera, Cornell University,
is currently visiting the department from October 2-November 1, 2004. His
visit is made possible by the Ordway Endowment. During his stay, Professor
Billera's office will be Vincent Hall 450. You can reach him by phone at 625-
7801.
The Institute of Mathematics and Its
Applications (IMA) is sponsoring a workshop on “Singularities in Materials".
Please see http://www.ima.umn.edu/matter/fall/singularities.html for further
information.
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Last Modified February 01, 2006 Contact the School of Mathematics The University of Minnesota is an equal opportunity educator and employer. © 2012, The Regents of the University of Minnesota |
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