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MiS Preprint

Quantitative homogenization of degenerate random environments

Arianna Giunti and Jean-Christophe Mourrat


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.

MSC Codes:
35B27, 35K65, 60K37
Quantitative homogenization, Environment viewed by the particle, Mixing of Markov chains, Corrector estimate

Related publications

2018 Repository Open Access
Arianna Giunti and Jean-Christophe Mourrat

Quantitative homogenization of degenerate random environments

In: Annales de l'Institut Henri Poincaré / B, 54 (2018) 1, pp. 22-50