Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 261-01. Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three
Manuscript map · lines 7635–7644
OpenAI@2026-10-07#rem:oai-p-261-01
Authors: OpenAI. Family 261.
Title: Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three.
Abstract: For each fixed dimension d ≥ 3 and each fixed sufficiently small positive disorder strength, we prove that the Anderson operator on ℤd with independent uniform site potentials almost surely has purely absolutely continuous spectrum with nonzero weight on an open energy interval. The interval may depend on d but is independent of the disorder strength. This settles the purely absolutely continuous energy-range question in Simon's Problem 1 for this model.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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