An edge CLT for the log determinant of Laguerre beta ensembles
Why this work is in the frame
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Bibliographic record
Abstract
Nous obtenons un TCL pour log|det(Mn−sn)|, où Mn est un ensemble beta Laguerre mis à l’échelle et où sn=d++σnn−2/3, avec d+ désignant la borne supérieure du spectre limite de Mn et σn désignant une fonction à croissance lente (loglog2n≪σn≪log2n). Dans les cas particuliers du LUE et du LOE, nous prouvons que le TCL reste valide lorsque σn est d’ordre constant. Un résultat similaire a été prouvé pour les matrices de Wigner par Johnstone, Klochkov, Onatski et Pavlyshyn. Ce type de TCL pour des matrices de Laguerre est intéressant pour les tests statistiques de matrices de covariance à perturbations critiques ainsi que d’énergie libre de verres de spin sphériques bipartites à température critique.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it