Abstract
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 language | English (US) |
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Article number | 28 |
Journal | Electronic Journal of Probability |
Volume | 22 |
DOIs | |
State | Published - 2017 |
Keywords
- Corrector
- Gaussian free field
- Markov property
- Stochastic homogenization
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty