Scaling limit of fluctuations in stochastic homogenization

Yu Gu; Jean Christophe Mourrat

doi:10.1137/15M1010683

Scaling limit of fluctuations in stochastic homogenization

Yu Gu, Jean Christophe Mourrat

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d ≥ 3 and for independent and identically distributed 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.

Original language	English (US)
Pages (from-to)	452-481
Number of pages	30
Journal	Multiscale Modeling and Simulation
Volume	14
Issue number	1
DOIs	https://doi.org/10.1137/15M1010683
State	Published - 2016

Keywords

Central limit theorem
Helffer Sjöstrand representation
Quantitative homogenization
Stein s method

ASJC Scopus subject areas

General Chemistry
Modeling and Simulation
Ecological Modeling
General Physics and Astronomy
Computer Science Applications

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10.1137/15M1010683

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abstract = "We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d ≥ 3 and for independent and identically distributed 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.",

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AU - Mourrat, Jean Christophe

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AB - We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d ≥ 3 and for independent and identically distributed 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.

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KW - Helffer Sjöstrand representation

KW - Quantitative homogenization

KW - Stein s method

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Scaling limit of fluctuations in stochastic homogenization

Abstract

Keywords

ASJC Scopus subject areas

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