随机算子本征值在局部相中的渐近遍历性
Asymptotic ergodicity of the eigenvalues of random operators in the localized phase
摘要：
证明了对于一般的随机算子，其局部化区域的展开特征值族在N的意义下是渐近遍历的。南（见[Mi：11]）。N. Minami证明了这是局域化区域中离散Anderson模型的情况。我们还提供了一个本地的模拟这一结果。从渐近遍历性，人们可以恢复的统计水平间距以及其他一些谱统计。我们的证明依赖于abs/1011.1832中的分析。
英文摘要：
We prove that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of N. Minami (see [Mi:11]). N. Minami conjectured this to be the case for discrete Anderson model in the localized regime. We also provide a local analogue of this result. From the asymptotics ergodicity, one can recover the statistics of the level spacings as well as a number of other spectral statistics. Our proofs rely on the analysis developed in abs/1011.1832.
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