Introductory program: A calculus for quantitative stochastic homogenization
Homogenization and Random Phenomenon
04 September 14:15 - 15:00
Felix Otto - Max Planck Institut
The qualitative theory of stochastic homogenization of uniformly elliptic linear (but possibly nonsymmetric) systems in divergence form is well-understood. Quantitative results on the speed of convergence, and on the error in the representative volume method, like recently obtained by Gloria, Neukamm, and Otto for scalar equations, require a type of stochastic regularity theory for the corrector (e.g. higher moment bounds). One of the main insight of the very recent work of Armstrong and Smart is that one should separate these error estimates, which require strong mixing conditions in order to yield optimal rates, from the (large scale) regularity theory for $a$-harmonic functions, which by the philosophy of Avellaneda and Lin from periodic homogenization are expected to hold under weak mixing conditions. We present a very recent result in this direction. This is joint work with Antoine Gloria and Stefan Neukamm.
KTH Royal Institute of Technology
The University of Chicago