Tracy–Widom distribution
E898464
The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Tracy–Widom distribution canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991190 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Tracy–Widom distribution Context triple: [random matrix theory, hasKeyConcept, Tracy–Widom distribution]
-
A.
Wigner surmise
The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
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B.
Gaussian unitary ensemble
The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
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C.
Jacobi ensemble
The Jacobi ensemble is a family of random matrix models whose eigenvalue distributions are supported on a finite interval and are closely connected to classical orthogonal polynomials and beta-type probability measures.
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D.
Gaussian orthogonal ensemble
The Gaussian orthogonal ensemble is a fundamental random matrix ensemble of real symmetric matrices with Gaussian-distributed entries, central to the study of eigenvalue statistics and universality in random matrix theory.
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E.
Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Tracy–Widom distribution Target entity description: The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
-
A.
Wigner surmise
The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
-
B.
Gaussian unitary ensemble
The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
-
C.
Jacobi ensemble
The Jacobi ensemble is a family of random matrix models whose eigenvalue distributions are supported on a finite interval and are closely connected to classical orthogonal polynomials and beta-type probability measures.
-
D.
Gaussian orthogonal ensemble
The Gaussian orthogonal ensemble is a fundamental random matrix ensemble of real symmetric matrices with Gaussian-distributed entries, central to the study of eigenvalue statistics and universality in random matrix theory.
-
E.
Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
distribution in random matrix theory
ⓘ
limiting distribution ⓘ probability distribution ⓘ |
| appearsIn |
combinatorial probability
ⓘ
growth models in the KPZ universality class ⓘ last passage percolation ⓘ longest increasing subsequence of random permutations ⓘ non-intersecting random walks ⓘ statistics of extreme eigenvalues ⓘ |
| arisesIn |
Gaussian orthogonal ensemble
NERFINISHED
ⓘ
Gaussian symplectic ensemble NERFINISHED ⓘ Gaussian unitary ensemble NERFINISHED ⓘ |
| belongsTo | universality class of edge eigenvalue fluctuations ⓘ |
| definedVia |
Fredholm determinant of the Airy kernel
ⓘ
solution of a Painlevé II differential equation ⓘ |
| describes | fluctuations of the largest eigenvalue of large random matrices ⓘ |
| field |
probability theory
ⓘ
random matrix theory ⓘ |
| generalizes | classical extreme value distributions for eigenvalues ⓘ |
| governs | edge scaling limit of eigenvalues ⓘ |
| hasAbbreviation | TW distribution NERFINISHED ⓘ |
| hasKurtosisExcess | approximately 0.16524294 for type II ⓘ |
| hasMean | approximately -1.2065335745820 for type II ⓘ |
| hasSkewness | approximately 0.293464524 for type II ⓘ |
| hasVariance | approximately 1.607781034581 for type II ⓘ |
| hasVariant |
Tracy–Widom distribution of type I
NERFINISHED
ⓘ
Tracy–Widom distribution of type II NERFINISHED ⓘ Tracy–Widom distribution of type III ⓘ |
| introducedBy |
Craig Tracy
NERFINISHED
ⓘ
Harold Widom NERFINISHED ⓘ |
| introducedIn | 1990s ⓘ |
| namedAfter |
Craig Tracy
NERFINISHED
ⓘ
Harold Widom NERFINISHED ⓘ |
| parameterizes | edge fluctuations of eigenvalues ⓘ |
| relatedTo |
Airy kernel
NERFINISHED
ⓘ
Gaussian ensembles NERFINISHED ⓘ Painlevé II equation NERFINISHED ⓘ Wigner matrices ⓘ Wishart matrices NERFINISHED ⓘ |
| support | subset of the real line ⓘ |
| tailBehavior |
asymmetric
ⓘ
stretched exponential decay ⓘ |
| usedFor | asymptotic distribution of the largest eigenvalue ⓘ |
| usedIn |
high-dimensional statistics
ⓘ
multivariate statistical testing ⓘ principal component analysis asymptotics ⓘ signal detection in noise ⓘ wireless communications theory ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Tracy–Widom distribution Description of subject: The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.