On generalized Gaussian free fields and stochastic homogenization

Yu Gu, Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review


We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an “effective fluctuation tensor” that we denote by Q. We prove an expansion of Q in the regime of small ellipticity ratio. This expansion shows that the scaling limit of the corrector is not necessarily a classical GFF, and in particular does not necessarily satisfy the Markov property.

Original languageEnglish (US)
Article number28
JournalElectronic Journal of Probability
StatePublished - 2017


  • Corrector
  • Gaussian free field
  • Markov property
  • Stochastic homogenization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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