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]

Complete list of metadatas

Cited literature [22 references] Display Hide Download

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
Long-term archiving on : Monday, March 20, 2017 - 4:02:18 PM

scale-limit.pdf

Files produced by the author(s)

Scaling Limit of Fluctuations in Stochastic Homogenization

Files

Identifiers

Collections

Citation

Export

Metrics

133

124

Contact

Scaling Limit of Fluctuations in Stochastic Homogenization

Files

Identifiers

Collections

Citation

Export

Share

Metrics

133

124

Contact