# Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization

2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : In the present contribution we establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy a spectral gap estimate in probability, and for $d>2$. The main difference with respect to the first part of [Gloria-Otto, arXiv:1409.0801] is that we avoid here the use of Green's functions and more directly rely on the De Giorgi-Nash-Moser theory.
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https://hal.inria.fr/hal-01060499
Contributor : Antoine Gloria <>
Submitted on : Wednesday, September 3, 2014 - 4:59:38 PM
Last modification on : Monday, August 20, 2018 - 9:44:02 AM
Long-term archiving on : Thursday, December 4, 2014 - 11:31:52 AM

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### Citation

Antoine Gloria, Felix Otto. Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization. ESAIM: PROCEEDINGS AND SURVEYS, 2014, pp.26. ⟨10.1051/proc/201448003⟩. ⟨hal-01060499⟩

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