Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian\n and Wishart matrices and Cyclic Fock spaces
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Bibliographic record
Abstract
We extend the relation between random matrices and free probability theory\nfrom the level of expectations to the level of fluctuations. We introduce the\nconcept of "second order freeness" and derive the global fluctuations of\nGaussian and Wishart random matrices by a general limit theorem for second\norder freeness. By introducing cyclic Fock space, we also give an operator\nalgebraic model for the fluctuations of our random matrices in terms of the\nusual creation, annihilation, and preservation operators. We show that\northogonal families of Gaussian and Wishart random matrices are asymptotically\nfree of second order.\n
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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