Affiliation:
1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
Abstract
We study stochastic homogenization for linear elliptic equations in divergence form and focus on the recently developed theory of fluctuations. It has been observed that the fluctuations of averages of the solution are captured by the so-called standard homogenization commutator Ξ ε o . Our aim is to study how Ξ ε o (and its higher-order analogs) decorrelates on large scales when averaged on balls which are far enough. Taking advantage of its approximate locality, we give a quantitative characterization of this decorrelation in terms of both the macroscopic scale and the distance between the balls showing that Ξ ε o inherits the correlation properties of the environment.
Reference17 articles.
1. The additive structure of elliptic homogenization;Armstrong;Invent. Math.,2017
2. S. Armstrong, T. Kuusi and J.-C. Mourrat, Quantitative Stochastic Homogenization and Large-Scale Regularity, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 352, Springer, Cham, 2019.
3. Quantitative stochastic homogenization of convex integral functionals;Armstrong;Ann. Sci. Éc. Norm. Supér. (4),2016
4. Scaling limit of the homogenization commutator for Gaussian coefficient fields;Duerinckx;Ann. Appl. Probab.,2022
5. Robustness of the pathwise structure of fluctuations in stochastic homogenization;Duerinckx;Probab. Theory Related Fields,2020