论文标题
Dietlein-Elgart之后的高级安德森模型的本地特征值统计
Local eigenvalue statistics for higher-rank Anderson models after Dietlein-Elgart
论文作者
论文摘要
我们使用Dietlein和Elgart（Arxiv：Arxiv：1712.03925）开发的特征值水平间距的方法来证明Anderson模型的本地特征值统计（LES）在$ Z^d $上，均与均匀级别的$ M \ m \ m \ m \ geq 2 $，单点求职$ n points $ n points n posity n hith n in n of n n thice n n hiter（n） $ n（e_0）$是在光谱带边缘附近本地化区域的能源$ e_0 $的状态密度。这改善了Hislop和Krishna（Arxiv：1809.01236）的结果，后者证明了LES是一个复合泊松过程，并在集合$ \ {1，2，\ ldots，m \} $上支持Lévy措施。我们的证明是Dieltein和Elgart的思想应用于具有两个光谱带边缘的这些更高级别的晶格模型，并在更简单的环境中说明了Dieltein和Elgart证明的关键步骤。
We use the method of eigenvalue level spacing developed by Dietlein and Elgart (arXiv:1712.03925) to prove that the local eigenvalue statistics (LES) for the Anderson model on $Z^d$, with uniform higher-rank $m \geq 2$, single-site perturbations, is given by a Poisson point process with intensity measure $n(E_0)~ds$, where $n(E_0)$ is the density of states at energy $E_0$ in the region of localization near the spectral band edges. This improves the result of Hislop and Krishna (arXiv:1809.01236), who proved that the LES is a compound Poisson process with Lévy measure supported on the set $\{1, 2, \ldots, m \}$. Our proofs are an application of the ideas of Dieltein and Elgart to these higher-rank lattice models with two spectral band edges, and illustrate, in a simpler setting, the key steps of the proof of Dieltein and Elgart.
