  We establish sublinear growth of correctors in the context of stochastic
homogenization of linear elliptic PDEs. In case of weak decorrelation and
"essentially Gaussian" coefficient fields, we obtain optimal (stretched
exponential) stochastic moments for the minimal radius above which the
corrector is sublinear. Our estimates also capture the quantitative
sublinearity of the corrector (caused by the quantitative decorrelation on
larger scales) correctly. The result is based on estimates on the Malliavin
derivative for certain functionals which are basically averages of the gradient
of the corrector, on concentration of measure, and on a mean value property for
$a$-harmonic functions.
