单格位分布与柯西分布卷积时Anderson模型积分态密度和能级统计的光滑性
Smoothness of integrated density of states and level statistics of the Anderson model when single site distribution is convolution with the Cauchy distribution
摘要：
在这项工作中，我们考虑$\ell^2(\mathbb{Z}^d)$上的Anderson模型时，单点分布（SSD）的$μ_1 * μ_2$，其中$μ_1$是柯西分布和$μ_2$是任何概率测度。对于这个模型，我们证明了积分态密度（IDS）是无穷可微的无序强度无关。此外，我们调查的本地特征值统计的$d\ge 2$，没有任何假设的本地化属性。
英文摘要：
In this work we consider the Anderson model on $\ell^2(\mathbb{Z}^d)$ when the single site distribution (SSD) is given by $μ_1 * μ_2$, where $μ_1$ is the Cauchy distribution and $μ_2$ is any probability measure. For this model we prove that the integrated density of states (IDS) is infinitely differentiable irrespective of the disorder strength. Also, we investigate the local eigenvalue statistics of this model in $d\ge 2$, without any assumption on the localization property.
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