Geodesic
Quantitative results on the corrector equation in stochastic homogenization
Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3489-3548.

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We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions d≥2. In previous works we studied the model problem of a discrete elliptic equation on Zd . Under the assumption that a spectral gap estimate holds in probability, we proved that there exists a stationary corrector field in dimensions d>2 and that the energy density of that corrector behaves as if it had finite range of correlation in terms of the variance of spatial averages – the latter decays at the rate of the central limit theorem. In this article we extend these results, and several other estimates, to the case of a continuum linear elliptic equation whose (not necessarily symmetric) coefficient field satisfies a continuum version of the spectral gap estimate. In particular, our results cover the example of Poisson random inclusions.
DOI : 10.4171/jems/745
Classification : 35-XX, 39-XX, 60-XX
Keywords: Stochastic homogenization, corrector equation, variance estimate 
@article{JEMS_2017_19_11_a6,
     author = {Antoine Gloria and Felix Otto},
     title = {Quantitative results on the corrector equation in stochastic homogenization},
     journal = {Journal of the European Mathematical Society},
     pages = {3489--3548},
     publisher = {mathdoc},
     volume = {19},
     number = {11},
     year = {2017},
     doi = {10.4171/jems/745},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/745/}
}
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Antoine Gloria; Felix Otto. Quantitative results on the corrector equation in stochastic homogenization. Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3489-3548. doi : 10.4171/jems/745. http://geodesic.mathdoc.fr/articles/10.4171/jems/745/

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