Open Access
2017 On generalized Gaussian free fields and stochastic homogenization
Yu Gu, Jean-Christophe Mourrat
Electron. J. Probab. 22: 1-21 (2017). DOI: 10.1214/17-EJP51


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.


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Yu Gu. Jean-Christophe Mourrat. "On generalized Gaussian free fields and stochastic homogenization." Electron. J. Probab. 22 1 - 21, 2017.


Received: 24 January 2016; Accepted: 20 March 2017; Published: 2017
First available in Project Euclid: 24 March 2017

zbMATH: 1359.60064
MathSciNet: MR3629872
Digital Object Identifier: 10.1214/17-EJP51

Primary: 35B27 , 35R60 , 60G60

Keywords: Corrector , Gaussian free field , Markov property , Stochastic homogenization

Vol.22 • 2017
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