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Record W3101379558

Moment determinants as isomonodromic tau functions

2013· article· en· W3101379558 on OpenAlexaff
Marco Bertola

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsConcordia University
Fundersnot available
KeywordsToeplitz matrixMathematicsRamanujan tau functionOrthogonalityRandom matrixPartition (number theory)Orthogonal polynomialsPure mathematicsClass (philosophy)Semiclassical physicsMatrix (chemical analysis)Moment (physics)Ramanujan's sumCombinatoricsEigenvalues and eigenvectors
DOInot available

Abstract

fetched live from OpenAlex

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated with certain classes of (multiple) orthogonal polynomials. The determinants include Hankel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants also appear as partition functions of random matrix models, including an instance of a two-matrix model.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

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)0.001
metaresearch head score (Gemma)0.002
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: Empirical
Teacher disagreement score0.005
Threshold uncertainty score0.016

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0020.001
Science and technology studies0.0010.002
Scholarly communication0.0020.001
Open science0.0000.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0050.001

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 head0.024
GPT teacher head0.306
Teacher spread0.282 · 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

Citations19
Published2013
Admission routes1
Has abstractyes

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