论文标题
限制d维随机施罗丁格操作员的极端特征值的分布
Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator
论文作者
论文摘要
We consider Schrödinger operator with random decaying potential on $\ell^2 ({\bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges to a inhomogeneous Poisson process, under certain condition on the single-site distribution, and (iii) there are “边界线”案例，使我们在上述（II）的意义上具有泊松统计，如果潜力不会衰减，而如果潜力确实衰减，则我们不会衰减。
We consider Schrödinger operator with random decaying potential on $\ell^2 ({\bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges to a inhomogeneous Poisson process, under certain condition on the single-site distribution, and (iii) there are "border-line" cases, such that we have Poisson statistics in the sense of (ii) above if the potential does not decay, while we do not if the potential does decay.
