Poisson statistics for one-dimensional Anderson--Bernoulli Schrödinger operators
Yi Han
Source abstract
We prove Poisson local eigenvalue statistics for one-dimensional Schrödinger operators with nondegenerate Bernoulli potentials at any fixed nonzero coupling. After unfolding by the integrated density of states (IDS), the local eigenvalue process converges to a Poisson point process of unit intensity at every energy in the interior of the almost-sure spectrum. The theorem also holds for bounded nonconstant iid potentials, provided the IDS is continuous and strictly increasing near the reference energy. If the IDS also has a finite positive derivative at that energy, the usual linear normalization gives the same limit. The proof uses a phase coordinate with exact IDS drift to obtain a uniform exponential crossing law and joint Poisson counts in disjoint energy windows.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.