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2015 Moment bounds for the corrector in stochastic homogenization of a percolation model
Agnes Lamacz, Stefan Neukamm, Felix Otto
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Electron. J. Probab. 20: 1-30 (2015). DOI: 10.1214/EJP.v20-3618


We study the corrector equation in stochastic homogenization for a simplified Bernoulli percolation model on $\mathbb{Z}^d$, $d > 2$. The model is obtained from the classical $\{0,1\}$-Bernoulli bond percolation by conditioning all bonds parallel to the first coordinate direction to be open. As a main result we prove (in fact for a slightly more general model) that stationary correctors exist and that all finite moments of the corrector are bounded. This extends a previous result of Gloria & Otto, where uniformly elliptic conductances are treated, to the degenerate case. With regard to the associated random conductance model, we obtain as a side result that the corrector not only grows subinearly, but slower than any polynomial rate. Our argument combines a quantification of ergodicity by means of a Spectral Gap on Glauber dynamics with regularity estimates on the gradient of the elliptic Green's function.


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Agnes Lamacz. Stefan Neukamm. Felix Otto. "Moment bounds for the corrector in stochastic homogenization of a percolation model." Electron. J. Probab. 20 1 - 30, 2015.


Accepted: 14 October 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1326.39015
MathSciNet: MR3418538
Digital Object Identifier: 10.1214/EJP.v20-3618

Primary: 39A70
Secondary: 60F17, 60K37


Vol.20 • 2015
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