Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Jean Christophe Mourrat

Research output: Contribution to journalArticle

Abstract

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For smooth initial condition, the rescaled solution of such an equation, once averaged over the randomness, is shown to converge polynomially fast to the solution of the homogenized equation, with an explicit exponent depending only on the dimension. Polynomial rate of homogenization for the averaged heat kernel, with an explicit exponent, is then derived. Similar results for elliptic equations are also presented.

Original languageEnglish (US)
Pages (from-to)279-314
Number of pages36
JournalProbability Theory and Related Fields
Volume160
Issue number1-2
DOIs
StatePublished - 2013

Keywords

  • Central limit theorem
  • Martingale
  • Quantitative homogenization
  • Random walk in random environment

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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