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.