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We prove quantitative estimates for the stochastic homogenization of linearuniformly elliptic equations in nondivergence form. Under strong independenceassumptions on the coefficients, we obtain optimal estimates on thesubquadratic growth of the correctors with stretched exponential-type bounds inprobability. Like the theory of Gloria and Otto \cite{GO1,GO2} for divergenceform equations, the arguments rely on nonlinear concentration inequalitiescombined with certain estimates on the Green's functions and derivative boundson the correctors. We obtain these analytic estimates by developing a $C^{1,1}$regularity theory down to microscopic scale, which is of independent interestand is inspired by the $C^{0,1}$ theory introduced in the divergence form caseby the first author and Smart \cite{AS2}.

Optimal quantitative estimates in stochastic homogenization for elliptic equations in nondivergence form