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Record W1958800402 · doi:10.1214/154957806000000078

Determinantal Processes and Independence

2006· article· en· W1958800402 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueProbability Surveys · 2006
Typearticle
Languageen
FieldMathematics
TopicRandom Matrices and Applications
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of CanadaCanada Research ChairsNational Science Foundation
KeywordsMathematicsDeterminantal point processPoint processBernoulli's principleEigenvalues and eigenvectorsRandom variableSimple (philosophy)Random matrixMathematical proofCombinatoricsProjection (relational algebra)Bernoulli distributionBernoulli processCentral limit theoremProbability theoryPure mathematicsGeometryStatistics

Abstract

fetched live from OpenAlex

We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees). They have the striking property that the number of points in a region D is a sum of independent Bernoulli random variables, with parameters which are eigenvalues of the relevant operator on L2(D). Moreover, any determinantal process can be represented as a mixture of determinantal projection processes. We give a simple explanation for these known facts, and establish analogous representations for permanental processes, with geometric variables replacing the Bernoulli variables. These representations lead to simple proofs of existence criteria and central limit theorems, and unify known results on the distribution of absolute values in certain processes with radially symmetric distributions.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Observational · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.777
Threshold uncertainty score0.310

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.039
GPT teacher head0.295
Teacher spread0.256 · 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