Felix Otto, MPI für Mathematik in den Naturwissenschaften, Leipzig
Effective behavior of random media
Felix Otto will speak as invited guest during this joint colloquium of SFB 1114 and SFB 1294 on the Effective Behavior of random media Abstract: In engineering applications, heterogeneous media are often described in statistical terms. This partial knowledge is sucient to determine the effective, i. e. large-scale behavior. This effective behavior may be inferred from the Representative Volume Element (RVE) method. I report on last years' progress on the quantitative understanding of what is called stochastic homogenization of elliptic partial differential equations: optimal error estimates of the RVE method, leading-order characterization of fluctuations, effective multipole expansions. Methods connect to elliptic regularity theory and to concentration of measure arguments.