  This paper is the companion article to [Ann. Probab. 39 (2011) 779--856]. We
consider a discrete elliptic equation on the $d$-dimensional lattice
$\mathbb{Z}^d$ with random coefficients $A$ of the simplest type: They are
identically distributed and independent from edge to edge. On scales large
w.r.t. the lattice spacing (i.e., unity), the solution operator is known to
behave like the solution operator of a (continuous) elliptic equation with
constant deterministic coefficients. This symmetric "homogenized" matrix
$A_{\mathrm{hom}}=a_{\mathrm{hom}}\mathrm{Id}$ is characterized by $\xi\cdot
A_{\mathrm{hom}}\xi=<(\xi+\nabla\phi)\cdot A(\xi+\nabla\phi)>$ for any
direction $\xi\in\mathbb{R}^d$, where the random field $\phi$ (the "corrector")
is the unique solution of $-\nabla^*\cdot A(\xi+\nabla\phi)=0$ in
$\mathbb{Z}^d$ such that $\phi(0)=0$, $\nabla\phi$ is stationary and
$<\nabla\phi>=0$, $<\cdot>$ denoting the ensemble average (or expectation).
