Scaling limit of fluctuations in stochastic homogenization

Yu Gu, Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review


We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d ≥ 3 and for independent and identically distributed coefficients, we show that after a suitable scaling, these fluctuations converge to a Gaussian field that locally resembles a (generalized) Gaussian free field. The paper begins with a heuristic derivation of the result, which can be read independently and was obtained jointly with Scott Armstrong.

Original languageEnglish (US)
Pages (from-to)452-481
Number of pages30
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2016


  • Central limit theorem
  • Helffer Sjöstrand representation
  • Quantitative homogenization
  • Stein s method

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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