Pointwise two-scale expansion for parabolic equations with random coefficients

Abstract

We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.

25 pages. Minor revisions, to appear in PTRF

References in corpus (4)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Correlation structure of the corrector in stochastic homogenization
• Quantitative stochastic homogenization of convex integral functionals
• Noise-stability and central limit theorems for effective resistance of random electric networks

Cited by in corpus (2)

• Scaling limit of fluctuations in stochastic homogenization
• A central limit theorem for fluctuations in one dimensional stochastic homogenization