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• W1876010218 abstract "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." @default.
• W1876010218 created "2016-06-24" @default.
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• W1876010218 date "2015-01-01" @default.
• W1876010218 modified "2023-10-14" @default.
• W1876010218 title "Moment bounds for the corrector in stochastic homogenization of a percolation model" @default.
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• W1876010218 doi "https://doi.org/10.1214/ejp.v20-3618" @default.
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