Scaling limit of fluctuations in stochastic homogenization

Abstract

We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension $d\ge 3$ and for i.i.d.\ coefficients, we show that after a suitable scaling, these fluctuations converge to a Gaussian field that locally resembles a (generalized) Gaussian free field. The paper begins with a heuristic derivation of the result, which can be read independently and was obtained jointly with Scott Armstrong.

27 pages, revised version with a new section obtained jointly with Scott Armstrong

References in corpus (6)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Quantitative results on the corrector equation in stochastic homogenization
• Quantitative stochastic homogenization of convex integral functionals
• Normal approximation for the net flux through a random conductor
• A central limit theorem for fluctuations in one dimensional stochastic homogenization
• A quantitative central limit theorem for the effective conductance on the discrete torus

Cited by in corpus (5)

• The additive structure of elliptic homogenization
• Fluctuations in the Homogenization of Semilinear Equations with Random Potentials
• Eigenvalue fluctuations for random elliptic operators in homogenization regime
• Scaling limits of energies and correctors
• A central limit theorem for fluctuations in one dimensional stochastic homogenization