Spectral measure and approximation of homogenized coefficients

Antoine Gloria, Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review

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 ≥ 2, there exists an explicit numerical strategy to approximate homogenized coefficients which converges at the rate of the central limit theorem.

Original languageEnglish (US)
Pages (from-to)287-326
Number of pages40
JournalProbability Theory and Related Fields
Volume154
Issue number1-2
DOIs
StatePublished - 2012

Keywords

  • Ergodic theory
  • Numerical method
  • Spectral theory
  • Stochastic homogenization

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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