SCALING LIMIT OF FLUCTUATIONS IN STOCHASTIC HOMOGENIZATION

We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d >= 3 and for independent and identically distributed 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.