Abstract In a recent work, Bourgain gave a fine description of the expectation of solutions of discrete linear elliptic equations on with random coefficients in a perturbative regime using tools from harmonic analysis. This result is surprising for it goes beyond the expected accuracy suggested by recent results in quantitative stochastic homogenization. In this short article we reformulate Bourgain’s result in a form that highlights its interest to the state-of-the-art in homogenization (and especially the theory of fluctuations), and we state several related conjectures.

中文翻译：

---

对 Bourgain 在均质化中的惊人结果的评论

摘要 在最近的一项工作中，Bourgain 使用调和分析的工具对微扰状态下具有随机系数的离散线性椭圆方程的解的期望进行了精细的描述。这个结果令人惊讶，因为它超出了定量随机同质化的最新结果所建议的预期准确性。在这篇简短的文章中，我们以一种形式重新表述 Bourgain 的结果，强调其对同质化（尤其是波动理论）的最新技术的兴趣，并陈述了几个相关的猜想。