Quantitative homogenization of degenerate random environments

Arianna Giunti, Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review

Abstract

We study discrete linear divergence-form operators with random coefficients, also known as random conductance models. 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.

Original languageEnglish (US)
Pages (from-to)22-50
Number of pages29
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume54
Issue number1
DOIs
StatePublished - Feb 2018

Keywords

  • Corrector estimate
  • Environment viewed by the particle
  • Mixing of Markov chains
  • Quantitative homogenization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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