H”lder Continuity of the Integrated Density of States in the One-dimensional Anderson Model
Bibliographic record
Abstract
In this paper we consider the one-dimensional Anderson model for Random Schrödinger operators Hω = H0 + σVω and study the continuity properties of the integrated density of states. We prove that for any γ > 0, the IDS is Hölder continuous on (−2 + γ,−γ ) ∪ ( γ,2 − γ ), with exponent 1 − Cσ/γ with the constant C depending on the energy. We make only the weak assumption that the distribution of the noise has bounded support. This improves upon the work of Bourgain giving a non-quantitative bound to show that the exponent of Hölder continuity tends to 1 as σ ↓ 0; it is also more general as Bourgain's work was in the more specific Anderson-Bernoulli model.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".