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We consider the corrector equation from the stochastic homogenization ofuniformly elliptic finite-difference equations with random, possiblynon-symmetric coefficients. Under the assumption that the coefficients arestationary and ergodic in the quantitative form of a Logarithmic Sobolevinequality (LSI), we obtain optimal bounds on the corrector and its gradient indimensions $d \geq 2$. Similar estimates have recently been obtained in thespecial case of diagonal coefficients making extensive use of the maximumprinciple and scalar techniques. Our new method only invokes arguments that arealso available for elliptic systems and does not use the maximum principle. Inparticular, our proof relies on the LSI to quantify ergodicity and onregularity estimates on the derivative of the discrete Green's function inweighted spaces.

Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations