Pointwise two-scale expansion for parabolic equations with random coefficients

Yu Gu, Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review


We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension 3 and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.

Original languageEnglish (US)
Pages (from-to)585-618
Number of pages34
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - Oct 1 2016


  • Central limit theorem
  • Diffusion in random environment
  • Martingale
  • Quantitative homogenization

ASJC Scopus subject areas

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


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