Abstract
Recently, the quantification of errors in the stochastic homogenization of divergence-form operators has witnessed important progress. Our aim now is to go beyond error bounds, and give precise descriptions of the effect of the randomness, in the large-scale limit. This paper is a first step in this direction. Our main result is to identify the correlation structure of the corrector, in dimension 3 and higher. This correlation structure is similar to, but different from that of a Gaussian free field.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3207-3233 |
| Number of pages | 27 |
| Journal | Annals of Probability |
| Volume | 44 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2016 |
Keywords
- Homogenization
- Random media
- Two-point correlation function
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty