Year: 2026
Type: preprint
Abstract: For a one-dimensional discrete Schrödinger operator with bounded nonconstant iid potential, we prove a unit-intensity Poisson limit for local eigenvalues unfolded by the integrated density of states. The limit holds at every energy in the interior of the almost-sure spectrum. In particular, it holds for Bernoulli potentials at every fixed nonzero coupling. The proof uses auxiliary phase functions built from inverse stationary measures to obtain an exact IDS drift. Projective contraction then yields exponential crossing times, and a spatial subdivision argument gives independent Poisson counts in disjoint energy windows. At energies where the IDS has a finite positive derivative, the usual linear rescaling gives the same limit.
Source: arXiv (Cornell University)
Author: Han, Yi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222617805