能量的标度极限与修正因子
Scaling limits of energies and correctors
摘要：
在椭圆型方程的随机均匀化中，校正项起着核心作用。在有限的系数场依赖假设下，我们证明了校正器的大尺度空间平均值接近高斯自由场的一个变体。与以前的工作相比，参数不依赖于一个潜在的产品结构的概率测度。相反，我们依靠能量的可加性来证明这些的中心极限定理，并由此导出校正器的大尺度行为。
英文摘要：
In stochastic homogenization of elliptic equations, the corrector plays a central role. Under a finite range of dependence assumption on the coefficient field, we show that the large-scale spatial averages of the corrector approach those of a variant of the Gaussian free field. In contrast to previous work, the argument does not rely on an underlying product structure of the probability measure. Instead, we rely on the additivity of energy quantities to show central limit theorems for these, and derive the large-scale behavior of the corrector as a consequence.
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