Gaussian orthogonal ensemble
E443153
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.
All labels observed (5)
How this entity was disambiguated
This entity first appeared as the object of triple T4461547 — 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: Gaussian orthogonal ensemble Context triple: [Wigner surmise, ensembleType, Gaussian orthogonal ensemble]
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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.
random matrix theory
Random matrix theory is a branch of mathematics and mathematical physics that studies the statistical properties of matrices with randomly chosen entries, with deep applications to fields such as number theory, quantum chaos, and statistical mechanics.
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C.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
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D.
gauss
The gauss is a unit of magnetic flux density in the centimeter–gram–second (CGS) system, commonly used in physics to measure the strength of magnetic fields.
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E.
Wishart
Wishart is a Scottish surname historically associated with notable figures in religion, politics, and academia.
- 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: Gaussian orthogonal ensemble Target entity description: 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.
-
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.
random matrix theory
Random matrix theory is a branch of mathematics and mathematical physics that studies the statistical properties of matrices with randomly chosen entries, with deep applications to fields such as number theory, quantum chaos, and statistical mechanics.
-
C.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
D.
gauss
The gauss is a unit of magnetic flux density in the centimeter–gram–second (CGS) system, commonly used in physics to measure the strength of magnetic fields.
-
E.
Wishart
Wishart is a Scottish surname historically associated with notable figures in religion, politics, and academia.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Gaussian random matrix ensemble
ⓘ
probability distribution on matrices ⓘ random matrix ensemble ⓘ |
| abbreviation | GOE ⓘ |
| application |
disordered systems
ⓘ
mesoscopic physics ⓘ multivariate statistics ⓘ nuclear physics ⓘ number theory ⓘ quantum chaos ⓘ statistical mechanics ⓘ |
| belongsTo |
Wigner matrix ensembles
ⓘ
linked to:
Wigner matrices
|
| betaEnsembleParameter | 1 ⓘ |
| contrastWith |
Gaussian symplectic ensemble with beta equals 4
ⓘ
linked to:
Gaussian symplectic ensemble
Gaussian unitary ensemble with beta equals 2 ⓘ
linked to:
Gaussian unitary ensemble
|
| diagonalEntryVariance | twice off-diagonal variance in standard normalization ⓘ |
| DysonIndex | 1 ⓘ |
| edgeEigenvalueDistribution | Tracy–Widom distribution for beta equals 1 ⓘ |
| eigenvalueDensity | Wigner semicircle law ⓘ |
| eigenvalueStatistics |
Wigner–Dyson statistics
ⓘ
linked to:
Wigner surmise
|
| entryDistribution | Gaussian distribution ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| hasSymmetryGroup | orthogonal group O(n) ⓘ |
| introducedBy | Eugene Wigner ⓘ |
| invarianceProperty | invariant under orthogonal conjugation ⓘ |
| jointEigenvalueDensity | given by Vandermonde determinant to the first power times Gaussian weight ⓘ |
| levelRepulsionExponent | 1 ⓘ |
| matrixEntryMean | 0 ⓘ |
| matrixEntryVariance | depends on normalization convention ⓘ |
| matrixType | real symmetric matrices ⓘ |
| probabilityDensityForm | proportional to exp of minus n over 4 times trace of H squared in standard normalization ⓘ |
| relatedConcept |
Dyson Brownian motion
ⓘ
Gaussian symplectic ensemble ⓘ Gaussian unitary ensemble ⓘ orthogonal group ⓘ
linked to:
orthogonal group O(n)
|
| scalingLimit |
Airy kernel at the soft edge
ⓘ
sine kernel in the bulk ⓘ |
| spectralMeasureLimit | semicircle distribution ⓘ |
| symmetryClass | orthogonal symmetry ⓘ |
| timeReversalSymmetry | present ⓘ |
| typicalMatrixSize | n by n real symmetric matrix ⓘ |
| typicalNormalization | entries scaled by 1 over square root of matrix size ⓘ |
| universalityRole | prototype for universality of eigenvalue statistics ⓘ |
| usedFor | modeling spectra of time-reversal invariant quantum systems ⓘ |
| usedIn | universality proofs for Wigner matrices ⓘ |
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: Gaussian orthogonal ensemble Description of subject: 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.
Referenced by (15)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Gaussian orthogonal ensemble
Poisson distribution with P(s) = e^{-s}
→
comparedWith
→
Gaussian orthogonal ensemble spacing distribution
ⓘ
subject linked to:
Poisson distribution has P(s) = e^{-s}
linked to: Gaussian orthogonal ensemble
linked to: Gaussian orthogonal ensemble
linked to: Gaussian orthogonal ensemble
linked to: Gaussian orthogonal ensemble
linked to: Gaussian orthogonal ensemble
linked to: Gaussian orthogonal ensemble
linked to: Gaussian orthogonal ensemble
subject linked to:
Madame Tracy and Widom (Craig Tracy and Harold Widom)
linked to: Gaussian orthogonal ensemble