Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator

Abstract

We consider Schrödinger operator with random decaying potential on ${\ell }^2({\mathbf{Z}}^d)$ 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.

Some errors in published version are corrected

References in corpus (2)

• Eigenvectors of the critical 1-dimensional random Schroedinger operator
• Fluctuation of density of states for 1d Schrödinger operators