Gaussian symplectic ensemble
E444351
Gaussian ensemble
ensemble in random matrix theory
probability distribution on matrices
random matrix ensemble
The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gaussian Symplectic Ensemble | 1 |
| Gaussian symplectic ensemble canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4461549 — 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 symplectic ensemble Context triple: [Wigner surmise, ensembleType, Gaussian symplectic ensemble]
-
A.
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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B.
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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C.
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.
-
D.
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.
-
E.
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.
- 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 symplectic ensemble Target entity description: The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
Gaussian ensemble
ⓘ
ensemble in random matrix theory ⓘ probability distribution on matrices ⓘ random matrix ensemble ⓘ |
| abbreviation | GSE ⓘ |
| belongsToField |
mathematical physics
ⓘ
quantum chaos ⓘ random matrix theory ⓘ |
| contrastedWith |
Gaussian orthogonal ensemble (β = 1)
NERFINISHED
ⓘ
Gaussian unitary ensemble (β = 2) NERFINISHED ⓘ |
| hasAlternativeDescription | ensemble of complex 2N×2N Hermitian matrices with symplectic symmetry constraints ⓘ |
| hasApplicationsIn |
condensed matter physics
ⓘ
nuclear physics ⓘ quantum information theory ⓘ quantum transport ⓘ |
| hasCorrelationFunctions | expressible via quaternion determinants ⓘ |
| hasDysonClassLabel | β = 4 ⓘ |
| hasDysonIndex | 4 ⓘ |
| hasEdgeStatistics | Tracy–Widom distribution of type β = 4 for largest eigenvalue NERFINISHED ⓘ |
| hasEigenvalueRepulsionExponent | β = 4 ⓘ |
| hasEigenvalues | real ⓘ |
| hasGeneralization | non-Gaussian symplectic ensembles ⓘ |
| hasInvariance | invariant under conjugation by compact symplectic group ⓘ |
| hasJointEigenvalueDensity | proportional to exp(- (β/2) Σ λ_i^2 ) ∏_{i<j} |λ_i - λ_j|^β with β = 4 ⓘ |
| hasLevelRepulsion | P(s) ~ s^4 for small spacing s ⓘ |
| hasLevelSpacingStatistics | Wigner–Dyson distribution with β = 4 ⓘ |
| hasMatrixElementsDistribution | Gaussian in quaternion components ⓘ |
| hasMatrixSizeParameter | N ⓘ |
| hasMatrixType | self-dual quaternionic Hermitian matrices ⓘ |
| hasParameter | variance of matrix elements ⓘ |
| hasProbabilityDensityOnMatrices | proportional to exp(- (β/2) Tr H^2 ) with β = 4 ⓘ |
| hasSpectralMeasure | converges to Wigner semicircle law as N → ∞ ⓘ |
| hasSymmetryClass | symplectic symmetry ⓘ |
| hasSymmetryGroup | compact symplectic group Sp(N) ⓘ |
| hasTimeReversalSymmetry | true ⓘ |
| hasTypicalSymmetryClassLabel | class AII in Altland–Zirnbauer classification NERFINISHED ⓘ |
| hasUniversalityProperty | local eigenvalue statistics are universal in the bulk ⓘ |
| introducedBy | Freeman Dyson NERFINISHED ⓘ |
| introducedInContextOf | Dyson threefold way classification NERFINISHED ⓘ |
| isCompanionOf |
Gaussian orthogonal ensemble
NERFINISHED
ⓘ
Gaussian unitary ensemble NERFINISHED ⓘ |
| isOneOfDysonThreefoldWay | yes ⓘ |
| isPartOf | Wigner–Dyson ensembles NERFINISHED ⓘ |
| modelsSystemsWith | time-reversal symmetry and strong spin–orbit coupling ⓘ |
| relatedTo |
chiral Gaussian symplectic ensemble
ⓘ
symplectic Lie algebra ⓘ |
| usedToModel |
energy level statistics in complex nuclei
ⓘ
mesoscopic conductors with spin–orbit interaction ⓘ quantum systems with half-integer spin and time-reversal symmetry ⓘ systems with strong spin–orbit coupling ⓘ |
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 symplectic ensemble Description of subject: The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gaussian Symplectic Ensemble