Homogenization of non-divergence form operators in i.i.d. random environments

Abstract: We consider the convergence rate of a random non-divergence form difference equation on \$Z^d\$ to its "effective" differential equation on \$R^d\$. We will discuss the optimal convergence rate when the coefficient field has a finite range of dependence. Moreover, when the coefficient field is i.i.d., by exploiting the reflection symmetry of the distribution, we prove strictly faster convergence, improving the generic finite-range rate. Joint work with Hung V. Tran (Wisconsin) and Timo Sprekeler (Texas A&M)