Scaling Limit of Fluctuations in Stochastic Homogenization

Yu Gu; Jean-Christophe Mourrat

Scaling Limit of Fluctuations in Stochastic Homogenization

Yu Gu ¹ Jean-Christophe Mourrat ²

2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Abstract : We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d ⩾ 3 and for i.i.d. 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.

Keywords : quantitative homogenization central limit theorem Helffer-Sjöstrand representation Stein's method

Document type :

Journal articles

Domain :

Mathematics [math] / Analysis of PDEs [math.AP]

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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01401894
Contributor : Jean-Christophe Mourrat <>
Submitted on : Wednesday, November 23, 2016 - 10:37:32 PM
Last modification on : Friday, April 19, 2019 - 11:38:18 AM
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