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Recently, the quantification of errors in the stochastic homogenization ofdivergence-form operators has witnessed important progress. Our aim now is togo beyond error bounds, and give precise descriptions of the effect of therandomness, in the large-scale limit. This paper is a first step in thisdirection. Our main result is to identify the correlation structure of thecorrector, in dimension $3$ and higher. This correlation structure is similarto, but different from that of a Gaussian free field.

Correlation structure of the corrector in stochastic homogenization