  In the present contribution we establish quantitative results on the periodic
approximation of the corrector equation for the stochastic homogenization of
linear elliptic equations in divergence form, when the diffusion coefficients
satisfy a spectral gap estimate in probability, and for $d>2$. The main
difference with respect to the first part of [Gloria-Otto, arXiv:1409.0801] is
that we avoid here the use of Green's functions and more directly rely on the
De Giorgi-Nash-Moser theory.
