Journal
MULTISCALE MODELING & SIMULATION
Volume 14, Issue 1, Pages 452-481Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1010683
Keywords
quantitative homogenization; central limit theorem; Helffer-Sjostrand representation; Stein's method
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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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