逆隧穿估计及其在实直线上随机算子谱统计研究中的应用
Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
摘要：
我们提出了一个证明的Minami型估计的一维随机薛定谔算子有效的所有能量的本地化制度提供了一个韦格纳估计是已知的。然后将Minami型估计应用于各种模型，以获得其谱统计结果。我们证明Minami型估计的基本原理是，一维薛定谔算子的本征值要么与空间中彼此远离的本征函数相对应，要么来自某些隧穿现象。在第二种情况下，人们可以撤销隧道效应，从而构建在空间中彼此远离的准模式。
英文摘要：
We present a proof of Minami type estimates for one dimensional random Schrödinger operators valid at all energies in the localization regime provided a Wegner estimate is known to hold. The Minami type estimates are then applied to various models to obtain results on their spectral statistics. The heuristics underlying our proof of Minami type estimates is that close by eigenvalues of a one-dimensional Schrödinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena. In the second case, one can undo the tunneling and thus construct quasi-modes that live far away from each other in space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
