# Analysis Seminar

#### Higher Regularity in Stochastic Homogenization for Uniformly Elliptic Equations

**Speaker:**
Scott Armstrong

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, March 27, 2014, 11 a.m.

**Synopsis:**

We study uniformly elliptic equations with random coefficients satisfying a finite range of dependence. We show that, with overwhelming probability, solutions possess much higher regularity than can be expected in general for equations with rapidly coefficients. The statements take the form of a priori estimates, except that in place of universal constants are random variables which, while not almost surely bounded, but have quite good integrability in the probability space. These results can be thought of as stochastic, quantitative analogues of the results Avellaneda-Lin developed in the late 80s with compactness arguments. In the stochastic setting, we don't have compactness, but we do have concentration inequalities.