Gaussian unitary ensemble
E443666
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gaussian Unitary Ensemble | 2 |
| Gaussian unitary ensemble canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T4461548 — 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 unitary ensemble Context triple: [Wigner surmise, ensembleType, Gaussian unitary ensemble]
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
- 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 unitary ensemble Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
Gaussian ensemble
ⓘ
probability distribution ⓘ random matrix ensemble ⓘ unitary invariant ensemble ⓘ |
| alsoKnownAs | GUE NERFINISHED ⓘ |
| application |
mesoscopic physics
ⓘ
nuclear physics ⓘ number theory ⓘ quantum chaos ⓘ statistical mechanics ⓘ wireless communications ⓘ |
| belongsToClass | Wigner ensembles NERFINISHED ⓘ |
| bulkStatistics | described by sine kernel determinantal process ⓘ |
| DysonIndex | 2 ⓘ |
| edgeFluctuations | governed by Tracy–Widom GUE distribution ⓘ |
| eigenvalueCorrelation |
given by Airy kernel at soft edge
ⓘ
given by sine kernel in bulk scaling limit ⓘ |
| eigenvalueDistribution | determinantal point process ⓘ |
| eigenvalueJointDensity | proportional to exp(-Σ λ_i^2/2σ^2) Π_{i<j}(λ_i-λ_j)^2 ⓘ |
| entryDistribution | Gaussian-distributed entries ⓘ |
| entryIndependence | statistically independent entries ⓘ |
| field |
mathematical physics
ⓘ
quantum chaos ⓘ random matrix theory ⓘ |
| introducedBy | Freeman Dyson NERFINISHED ⓘ |
| invarianceProperty | invariant under conjugation by unitary matrices ⓘ |
| levelRepulsionExponent | 2 ⓘ |
| matrixType | complex Hermitian matrices ⓘ |
| parameter |
matrix size N
ⓘ
variance parameter of Gaussian entries ⓘ |
| probabilityDensityForm | proportional to exp(-Tr(H^2)/2σ^2) ⓘ |
| relatedConcept |
Airy kernel
NERFINISHED
ⓘ
Dyson Brownian motion NERFINISHED ⓘ Gaussian orthogonal ensemble NERFINISHED ⓘ Gaussian symplectic ensemble NERFINISHED ⓘ Tracy–Widom distribution NERFINISHED ⓘ Wigner semicircle law NERFINISHED ⓘ sine kernel ⓘ unitary group U(N) ⓘ |
| relatedTo | Riemann zeta function zeros (conjecturally similar statistics) ⓘ |
| symmetryClass | unitary symmetry ⓘ |
| timeReversalSymmetry | broken ⓘ |
| typicalEigenvalueDensity | Wigner semicircle distribution NERFINISHED ⓘ |
| universalityProperty | local eigenvalue statistics are universal in large N limit ⓘ |
| usedIn |
analysis of eigenvalue spacing distributions
ⓘ
study of spectral rigidity ⓘ theory of quantum transport ⓘ |
| usedToModel |
eigenvalue statistics of large complex Hermitian matrices
ⓘ
energy level statistics of quantum systems with broken time-reversal symmetry ⓘ |
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 unitary ensemble Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gaussian Unitary Ensemble
this entity surface form:
Gaussian Unitary Ensemble