Wigner matrices
E898468
Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Wigner matrices canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991208 — 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: Wigner matrices Context triple: [random matrix theory, hasKeyConcept, Wigner matrices]
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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.
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.
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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D.
Gaussian symplectic 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.
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E.
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.
- 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: Wigner matrices Target entity description: Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
-
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.
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.
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.
-
D.
Gaussian symplectic 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.
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E.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical object
ⓘ
random matrix ensemble ⓘ |
| appliesTo |
complex disordered quantum systems
ⓘ
models of heavy nuclei energy levels ⓘ |
| entryDistributionCondition |
diagonal entries are independent and identically distributed
ⓘ
entries have finite variance ⓘ off-diagonal entries are independent and identically distributed ⓘ off-diagonal entries are independent of diagonal entries ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| hasProperty |
centered entries (often mean zero)
ⓘ
complex Hermitian in the complex case ⓘ eigenvalues are real ⓘ identically distributed diagonal entries (possibly different law from off-diagonal) ⓘ identically distributed off-diagonal entries ⓘ independent entries up to symmetry ⓘ large dimension ⓘ real symmetric in the real case ⓘ symmetric or Hermitian ⓘ variance-normalized entries ⓘ |
| hasVariant |
Gaussian Orthogonal Ensemble
NERFINISHED
ⓘ
Gaussian Unitary Ensemble NERFINISHED ⓘ complex Hermitian Wigner matrices ⓘ real symmetric Wigner matrices ⓘ |
| introducedBy | Eugene Wigner NERFINISHED ⓘ |
| introducedInContext | statistical theory of energy levels of complex quantum systems ⓘ |
| namedAfter | Eugene Wigner NERFINISHED ⓘ |
| relatedTo |
Dyson Brownian motion
NERFINISHED
ⓘ
free probability theory ⓘ level repulsion ⓘ semicircle distribution ⓘ universality conjectures ⓘ |
| satisfies |
Wigner semicircle law for empirical spectral distribution
ⓘ
concentration of spectral norm around 2 in the normalized case ⓘ universality of local eigenvalue statistics under mild moment conditions ⓘ |
| scalingConvention | entries often scaled by 1/sqrt(n) ⓘ |
| typicalResult |
empirical spectral measure converges almost surely to semicircle law
ⓘ
fluctuations of largest eigenvalue often follow Tracy–Widom distribution ⓘ largest eigenvalue converges to 2 in the normalized case ⓘ local eigenvalue statistics in bulk match GOE or GUE statistics ⓘ |
| usedFor |
modeling energy levels of complex quantum systems
ⓘ
proving universality results in random matrix theory ⓘ studying delocalization of eigenvectors ⓘ studying eigenvalue statistics ⓘ studying global eigenvalue distribution ⓘ studying local eigenvalue spacing ⓘ studying spectral norms of random matrices ⓘ studying universal spectral behavior ⓘ |
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: Wigner matrices Description of subject: Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.