Scaling Limit of Fluctuations in Stochastic Homogenization

Yu Gu 1 Jean-Christophe Mourrat 2
1 Department of Mathematics [Stanford]
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
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Article dans une revue
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2016, 14, pp.452 - 481. 〈10.1137/15M1010683〉
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Yu Gu, Jean-Christophe Mourrat. Scaling Limit of Fluctuations in Stochastic Homogenization. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2016, 14, pp.452 - 481. 〈10.1137/15M1010683〉. 〈ensl-01401894〉

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