Electronic Journal of Probability

Moment bounds for the corrector in stochastic homogenization of a percolation model

Agnes Lamacz, Stefan Neukamm, and Felix Otto

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 106, 30 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067212

Digital Object Identifier
doi:10.1214/EJP.v20-3618

Mathematical Reviews number (MathSciNet)
MR3418538

Zentralblatt MATH identifier
1326.39015

Subjects
Primary: 39A70: Difference operators [See also 47B39]
Secondary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles

Keywords
quantitative stochastic homogenization percolation corrector

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Lamacz, Agnes; Neukamm, Stefan; Otto, Felix. Moment bounds for the corrector in stochastic homogenization of a percolation model. Electron. J. Probab. 20 (2015), paper no. 106, 30 pp. doi:10.1214/EJP.v20-3618. https://projecteuclid.org/euclid.ejp/1465067212


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