An optimal variance estimate in stochastic homogenization of discrete elliptic equations. (English) Zbl 1215.35025

This paper contains a fundamental theoretical result of clear practical importance: It estimates the dominant error when computing numerically the effective diffusion tensor (in a linear elliptic equation), when the original microscopic model is a discrete elliptic equation with random coefficients posed in a \(d\)-dimensional lattice. As far as we are aware, this is the first result of this type available in the literature. From the applications point of view, it would be very useful to see to which extent the authors’ working techniques are applicable beyond the linear setting.


35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
39A70 Difference operators
60H25 Random operators and equations (aspects of stochastic analysis)
60F99 Limit theorems in probability theory
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