### Abstract

We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension 3 and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.

Original language | English (US) |
---|---|

Pages (from-to) | 585-618 |

Number of pages | 34 |

Journal | Probability Theory and Related Fields |

Volume | 166 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2016 |

### Keywords

- Central limit theorem
- Diffusion in random environment
- Martingale
- Quantitative homogenization

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Pointwise two-scale expansion for parabolic equations with random coefficients'. Together they form a unique fingerprint.

## Cite this

Gu, Y., & Mourrat, J. C. (2016). Pointwise two-scale expansion for parabolic equations with random coefficients.

*Probability Theory and Related Fields*,*166*(1-2), 585-618. https://doi.org/10.1007/s00440-015-0667-z