标题： 随机安德森模型在谱边缘的增强Wegner和Minami估计及本征值统计 显示英文标题

标题： Enhanced Wegner and Minami estimates and eigenvalue statistics of random Anderson models at spectral edges

摘要： 我们考虑离散的安德森模型，并证明了增强的Wegner和Minami估计，其中区间长度被替换为在该区间上计算的IDS。 我们使用这些估计来改进之前论文中获得的有限体积本征值和本征函数的描述。 作为本征值和本征函数改进描述的结果，我们重新审视了局域化区域内谱统计的若干结果，并扩展了它们的有效范围，即： - 展开本征值的局部谱统计； - 展开本征值的局部渐近遍历性； 在维度1中，对于标准安德森模型，改进使我们能够在带边缘获得局部谱统计，即在Lifshitz尾部区域。 在高维情况下，这适用于修改后的安德森模型。 显示英文摘要

摘要： We consider the discrete Anderson model and prove enhanced Wegner and Minami estimates where the interval length is replaced by the IDS computed on the interval. We use these estimates to improve on the description of finite volume eigenvalues and eigenfunctions obtained in a previous paper. As a consequence of the improved description of eigenvalues and eigenfunctions, we revisit a number of results on the spectral statistics in the localized regime and extend their domain of validity, namely : - the local spectral statistics for the unfolded eigenvalues; - the local asymptotic ergodicity of the unfolded eigenvalues; In dimension 1, for the standard Anderson model, the improvement enables us to obtain the local spectral statistics at band edge, that is in the Lifshitz tail regime. In higher dimensions, this works for modified Anderson models.