论文标题
多维安德森模型的光谱波动
Spectral fluctuations for the multi-dimensional Anderson model
论文作者
论文摘要
在本文中，我们检查了$ \ mathbb {z}^d $在$ \ mathbb {z}^d $上的多项式线性统计的波动。我们证明，如果通过截短操作员大小的平方根进行标准化，这些波动会收敛到高斯极限。对于绝大多数潜力和多项式，我们表明限制分布的差异严格是积极的，我们完全对不发生这种情况的罕见情况进行了分类。
In this paper, we examine fluctuations of polynomial linear statistics for the Anderson model on $\mathbb{Z}^d$ for any potential with finite moments. We prove that if normalized by the square root of the size of the truncated operator, these fluctuations converge to a Gaussian limit. For a vast majority of potentials and polynomials, we show that the variance of the limiting distribution is strictly positive, and we classify in full the rare cases in which this does not happen.
