On the Bourgain-Spencer conjecture in stochastic homogenization

Meeting ID: 862 9472 2722
Passcode: 248678

Title: On the Bourgain-Spencer conjecture in stochastic homogenization

Abstract: In the context of stochastic homogenization, the so-called Bourgain-Spencer conjecture states that the ensemble-averaged solution of a divergence-form linear elliptic equation with random coefficients allows for an intrinsic description in terms of higher-order homogenized equations with an accuracy four times better than the almost sure solution itself. While previous rigorous results are restricted to a perturbative regime with small ellipticity ratio, we shall explain how half of the conjecture can be further proven in a non-perturbative regime. Our approach involves the construction of a new corrector theory in stochastic homogenization: while only a bounded number of correctors can be constructed as L^2 random fields, we show that twice as many can be usefully defined in a Schwartz-like distributional sense on the probability space.