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Record W591099569 · doi:10.1017/cbo9780511735127

Lectures on the Combinatorics of Free Probability

2006· book· en· W591099569 on OpenAlexaff
Alexandru Nica, Roland Speicher

Bibliographic record

VenueCambridge University Press eBooks · 2006
Typebook
Languageen
FieldMathematics
TopicRandom Matrices and Applications
Canadian institutionsQueen's UniversityUniversity of Waterloo
Fundersnot available
KeywordsFree probabilityProbability theoryMathematicsContext (archaeology)Class (philosophy)Operator (biology)Algebra of random variablesApplied probabilityProbability distributionAlgebra over a fieldRandom variableDiscrete mathematicsComputer scienceConvergence of random variablesPure mathematicsArtificial intelligence

Abstract

fetched live from OpenAlex

Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.

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)0.000
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: Methods · Consensus signal: none
Teacher disagreement score0.043
Threshold uncertainty score0.143

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.002
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.002
Science and technology studies0.0010.001
Scholarly communication0.0030.004
Open science0.0010.001
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0430.014

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 head0.034
GPT teacher head0.223
Teacher spread0.189 · 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
GenreMethods

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

Citations1,086
Published2006
Admission routes1
Has abstractyes

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