Variance decay for functionals of the environment viewed by the particle

Jean Christophe Mourrat

Research output: Contribution to journalArticle

Abstract

For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions, our results imply an estimate of the speed of convergence of the mean square displacement of the walk towards its limit.

Original languageEnglish (US)
Pages (from-to)294-327
Number of pages34
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume47
Issue number1
DOIs
StatePublished - Feb 2011

Keywords

  • Algebraic convergence to equilibrium
  • Environment viewed by the particle
  • Homogenization
  • Random walk in random environment

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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