Wigner semicircle law
E898462
The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Wigner semicircle law canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991183 — 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 semicircle law Context triple: [random matrix theory, hasKeyConcept, Wigner semicircle law]
-
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.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
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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.
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.
- 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 semicircle law Target entity description: The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
-
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.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
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.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
limit theorem
ⓘ
probability law ⓘ theorem in random matrix theory ⓘ |
| appliesTo |
large random Hermitian matrices
ⓘ
large random symmetric matrices ⓘ |
| assumes |
finite variance entries
ⓘ
identically distributed off-diagonal entries ⓘ independent matrix entries up to symmetry ⓘ mean-zero entries ⓘ |
| concernsLimit | matrix size n → ∞ ⓘ |
| concernsObject | Wigner matrices NERFINISHED ⓘ |
| concernsQuantity |
eigenvalue density
ⓘ
spectral measure ⓘ |
| describes |
empirical spectral distribution of eigenvalues
ⓘ
limiting eigenvalue distribution of random matrices ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| hasAlternativeName |
Wigner’s semicircle distribution
NERFINISHED
ⓘ
semicircular law NERFINISHED ⓘ |
| hasConvergenceType |
almost sure convergence
GENERATED
ⓘ
weak convergence of measures GENERATED ⓘ |
| hasDensityFormula | (1/(2πσ²))·sqrt(4σ² - x²) on [-2σ,2σ] ⓘ |
| hasDensityShape | semicircle ⓘ |
| hasGeneralization | free central limit theorem NERFINISHED ⓘ |
| hasParameter | variance parameter σ² ⓘ |
| hasSupport | compact interval ⓘ |
| hasSymmetry | symmetric density around 0 ⓘ |
| hasTypicalSupportForm | [-2σ, 2σ] ⓘ |
| holdsFor |
Gaussian Orthogonal Ensemble
NERFINISHED
ⓘ
Gaussian Symplectic Ensemble NERFINISHED ⓘ Gaussian Unitary Ensemble NERFINISHED ⓘ |
| implies | convergence of empirical spectral distribution ⓘ |
| introducedBy | Eugene Wigner NERFINISHED ⓘ |
| isAnalogOf | central limit theorem for eigenvalues ⓘ |
| isSpecialCaseOf | universality phenomena in random matrices ⓘ |
| mathematicalDomain |
matrix analysis
ⓘ
spectral theory ⓘ |
| namedAfter | Eugene Wigner NERFINISHED ⓘ |
| relatedTo |
Marchenko–Pastur law
NERFINISHED
ⓘ
circular law ⓘ free probability theory ⓘ |
| usedIn |
nuclear physics
ⓘ
number theory ⓘ quantum chaos ⓘ statistics of large data matrices ⓘ theory of disordered systems ⓘ |
| yearIntroducedApprox | 1950s ⓘ |
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 semicircle law Description of subject: The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.