Locality properties of standard homogenization commutator

TL;DR

This paper investigates how the standard homogenization commutator, a key random field in fluctuation theory, loses correlation over large spatial scales, enhancing understanding of its locality properties.

Contribution

It provides a quantitative analysis of the decorrelation behavior of the homogenization commutator at large scales, a novel insight in homogenization theory.

Findings

Demonstrates decay of correlations of the commutator over large distances

Provides quantitative estimates for decorrelation rates

Enhances understanding of fluctuation behavior in homogenization

Abstract

In the present work we study how the standard homogenization commutator, a random field that plays a central role in the theory of fluctuations, quantitatively decorrelates on large scales.