Quantitative homogenization of degenerate random environments
Arianna Giunti and Jean-Christophe Mourrat
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Submission date: 12. Mar. 2016
published in: Annales de l'Institut Henri Poincaré / B, 54 (2018) 1, p. 22-50
DOI number (of the published article): 10.1214/16-AIHP793
MSC-Numbers: 35B27, 35K65, 60K37
Keywords and phrases: Quantitative homogenization, Environment viewed by the particle, Mixing of Markov chains, Corrector estimate
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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.