  In a recent work, Bourgain gave a fine description of the expectation of
solutions of discrete linear elliptic equations on $\mathbb Z^d$ with random
coefficients in a perturbative regime using tools from harmonic analysis. This
result is surprising for it goes beyond the expected accuracy suggested by
recent results in quantitative stochastic homogenization. In this short article
we reformulate Bourgain's result in a form that highlights its interest to the
state-of-the-art in homogenization (and especially the theory of fluctuations),
and we state several related conjectures.
