Skip to Main content Skip to Navigation
Journal articles

Spectral measure and approximation of homogenized coefficients

Abstract : This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation formula to design and analyze effective and computable approximations of the homogenized coefficients. In particular, we show that information on the edge of the spectrum of the generator of the environment viewed by the particle projected on the local drift yields bounds on the approximation error, and conversely. Combined with results by Otto and the first author in low dimension, and results by the second author in high dimension, this allows us to prove that for any dimension $d\geq 2$, there exists an explicit numerical strategy to approximate homogenized coefficients which converges at the rate of the central limit theorem.
Document type :
Journal articles
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download
Contributor : Antoine Gloria Connect in order to contact the contributor
Submitted on : Sunday, May 22, 2011 - 10:51:55 AM
Last modification on : Wednesday, March 23, 2022 - 3:50:58 PM
Long-term archiving on: : Tuesday, August 23, 2011 - 2:20:45 AM


Files produced by the author(s)



Antoine Gloria, Jean-Christophe Mourrat. Spectral measure and approximation of homogenized coefficients. Probability Theory and Related Fields, Springer Verlag, 2012, 154, pp.287-326. ⟨10.1007/s00440-011-0370-7⟩. ⟨inria-00510513v2⟩



Record views


Files downloads