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The Distribution of the Largest Eigenvalue in the Gaussian Ensembles: β = 1, 2, 4

2000· book-chapter· en· W166475061 on OpenAlexaff
Craig A. Tracy, Harold Widom

Bibliographic record

Venuenot available
Typebook-chapter
Languageen
FieldMathematics
TopicRandom Matrices and Applications
Canadian institutionsMcGill University
Fundersnot available
KeywordsGaussianUniversality (dynamical systems)Unitary stateEigenvalues and eigenvectorsSymplectic geometryScalingStatistical physicsMathematicsLimitingFocus (optics)Distribution (mathematics)Distribution functionGaussian functionScaling limitPhysicsMathematical physicsPure mathematicsMathematical analysisQuantum mechanicsGeometry

Abstract

fetched live from OpenAlex
No abstract in any covered source. Its absence is recorded, not treated as a negative.

No abstract. This is not a gap in this database; OpenAlex has none either. 23.3% of the frame is in this state, and the screen finds HALF as much metaresearch here, so the absence is a measured bias rather than a missing field.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.012
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.008
Threshold uncertainty score0.028

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.012
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0020.001
Science and technology studies0.0010.003
Scholarly communication0.0020.004
Open science0.0010.001
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0080.002

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.

Opus teacher head0.029
GPT teacher head0.275
Teacher spread0.246 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations59
Published2000
Admission routes1
Has abstractno

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