My talk aims to present a quantitative version of the theory of stochastic homogenization via logarithmic Sobolev inequalities (LSI). After a brief overview of the main concepts, we introduce the homogenization problem. Then, we discuss the main role of the corrector's functions showing their main properties. In particular, we show their higher integrability as a consequence of a LSI. In the last part, we state the Gloria-Neukamm-Otto theorem.
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