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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Quantitative homogenization of degenerate random environments
Arianna Giunti and Jean-Christophe MourratAbstract
We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the orientation of the associated edge. We give a simple necessary and sufficient condition for the relaxation of the environment seen by the particle to be diffusive, in the sense of every polynomial moment. As a consequence, we derive polynomial moment estimates on the corrector.
- Received:
- 12.03.16
- Published:
- 24.03.16
- MSC Codes:
- 35B27, 35K65, 60K37
- Keywords:
- Quantitative homogenization, Environment viewed by the particle, Mixing of Markov chains, Corrector estimate