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 $\mathsf{Q} $. We prove an expansion of $\mathsf{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.
Citation
Yu Gu. Jean-Christophe Mourrat. "On generalized Gaussian free fields and stochastic homogenization." Electron. J. Probab. 22 1 - 21, 2017. https://doi.org/10.1214/17-EJP51
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