  We derive optimal estimates in stochastic homogenization of linear elliptic
equations in divergence form in dimensions $d\ge 2$. In previous works we
studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$.
Under the assumption that a spectral gap estimate holds in probability, we
proved that there exists a stationary corrector field in dimensions $d>2$ and
that the energy density of that corrector behaves as if it had finite range of
correlation in terms of the variance of spatial averages - the latter decays at
the rate of the central limit theorem. In this article we extend these results,
and several other estimates, to the case of a continuum linear elliptic
equation whose (not necessarily symmetric) coefficient field satisfies a
continuum version of the spectral gap estimate. In particular, our results
cover the example of Poisson random inclusions.
