标题： 随机薛定谔算子在伯努利分布势中的Lifschitz尾部 显示英文标题

标题： Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials

摘要： 本文提出了一个关于具有伯努利分布势的随机离散薛定谔算子的Lifschitz尾部行为的初等证明。 该证明通过在势取较低值的地方支持的正弦波的特征值来近似低特征值。 这是受到这样的想法的启发，即与低特征值相关的特征向量对势值的跳跃反应，就好像间隙是无限的一样。 显示英文摘要

摘要： This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schr\"{o}dinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the gap were infinite.