# An optimal variance estimate in stochastic homogenization of discrete elliptic equations

@article{Gloria2011AnOV, title={An optimal variance estimate in stochastic homogenization of discrete elliptic equations}, author={Antoine Gloria and Felix Otto}, journal={Annals of Probability}, year={2011}, volume={39}, pages={779-856} }

We consider a discrete elliptic equation with random coefficients $A$, which (to fix ideas) are identically distributed and independent from grid point to grid point $x\in\mathbb{Z}^d$. On scales large w.\ r.\ t.\ the grid size (i.\ e.\ unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic equation with constant deterministic coefficients. These symmetric ''homogenized'' coefficients $A_{hom}$ are characterized by % $$ \xi\cdot A_{hom}\xi…

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