  Corrector estimates constitute a key ingredient in the derivation of optimal
convergence rates via two-scale expansion techniques in homogenization theory
of random uniformly elliptic equations. The present work follows up - in terms
of corrector estimates - on the recent work of Fischer and Neukamm
(arXiv:1908.02273) which provides a quantitative stochastic homogenization
theory of nonlinear uniformly elliptic equations under a spectral gap
assumption. We establish optimal-order estimates (with respect to the scaling
in the ratio between the microscopic and the macroscopic scale) for
higher-order linearized correctors. A rather straightforward consequence of the
corrector estimates is the higher-order regularity of the associated
homogenized monotone operator.
