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arXiv · 1503.00578

Scaling limit of fluctuations in stochastic homogenization

Yu Gu·Jean-Christophe Mourrat
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Abstract

We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension $d\geq 3$ 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.

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Yu Gu, Jean-Christophe Mourrat. 2015-03-02. Scaling limit of fluctuations in stochastic homogenization. https://arxiv.org/abs/1503.00578

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