An edge CLT for the log determinant of Laguerre beta ensembles
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.020 | 0.004 |
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 source (direct Gemma or distilled Codex), 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".