Ginibre ensemble
E898467
The Ginibre ensemble is a fundamental class of non-Hermitian random matrices with independently distributed complex (or real/quaternion) Gaussian entries, widely studied for its rich eigenvalue statistics in random matrix theory.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Ginibre ensemble canonical | 1 |
| Ginibre point process | 1 |
| complex Ginibre ensemble | 1 |
| quaternion Ginibre ensemble | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991207 — 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: Ginibre ensemble Context triple: [random matrix theory, hasKeyConcept, Ginibre 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.
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.
Jacobi ensemble
The Jacobi ensemble is a family of random matrix models whose eigenvalue distributions are supported on a finite interval and are closely connected to classical orthogonal polynomials and beta-type probability measures.
-
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.
-
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: Ginibre ensemble Target entity description: The Ginibre ensemble is a fundamental class of non-Hermitian random matrices with independently distributed complex (or real/quaternion) Gaussian entries, widely studied for its rich eigenvalue statistics in 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.
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.
Jacobi ensemble
The Jacobi ensemble is a family of random matrix models whose eigenvalue distributions are supported on a finite interval and are closely connected to classical orthogonal polynomials and beta-type probability measures.
-
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.
-
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 (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
probability distribution on matrices ⓘ random matrix ensemble ⓘ |
| contrastWith |
Gaussian Unitary Ensemble (Hermitian)
ⓘ
linked to:
Gaussian unitary ensemble
Hermitian Wigner ensembles ⓘ |
| eigenvalueCorrelation | determinantal point process (complex case) ⓘ |
| eigenvalueDensityLimit | uniform on unit disk after appropriate scaling ⓘ |
| eigenvalueRepulsion | present ⓘ |
| eigenvalues | generally complex ⓘ |
| eigenvalueSupport | disk of radius 1 in large-N limit (after scaling) ⓘ |
| entryMean | 0 ⓘ |
| entryVariance | 1 ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| hasProperty |
entries are independent but not identically distributed under some normalizations
ⓘ
non-normal matrices ⓘ rotationally invariant eigenvalue distribution in complex plane (complex case) ⓘ |
| hasVariant |
complex Ginibre ensemble
ⓘ
linked to:
Ginibre ensemble
quaternion Ginibre ensemble ⓘ
linked to:
Ginibre ensemble
real Ginibre ensemble ⓘ |
| introducedBy | Jean Ginibre ⓘ |
| introducedInYear | 1965 ⓘ |
| isA | non-Hermitian random matrix ensemble ⓘ |
| matrixEntriesDistribution |
independent Gaussian entries
ⓘ
independent identically distributed complex Gaussian entries ⓘ independent identically distributed quaternion Gaussian entries ⓘ independent identically distributed real Gaussian entries ⓘ |
| namedAfter | Jean Ginibre ⓘ |
| publication | Ginibre 1965 Journal of Mathematical Physics paper ⓘ |
| relatedConcept |
Gaussian Orthogonal Ensemble
ⓘ
linked to:
Gaussian orthogonal ensemble
Gaussian Symplectic Ensemble ⓘ
linked to:
Gaussian symplectic ensemble
Gaussian Unitary Ensemble ⓘ
linked to:
Gaussian unitary ensemble
Ginibre point process ⓘ
linked to:
Ginibre ensemble
circular law ⓘ non-Hermitian spectral statistics ⓘ |
| scalingLimit | circular law for eigenvalues ⓘ |
| studiedFor |
complex eigenvalue correlations
ⓘ
eigenvalue spacing statistics ⓘ universality of non-Hermitian spectra ⓘ |
| symmetryClass | non-Hermitian ⓘ |
| typicalMatrixSize | N by N ⓘ |
| typicalNormalization | entries scaled by 1/sqrt(N) ⓘ |
| usedIn |
non-Hermitian operator theory
ⓘ
open quantum systems ⓘ quantum chaos ⓘ statistical physics ⓘ wireless communications modeling ⓘ |
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: Ginibre ensemble Description of subject: The Ginibre ensemble is a fundamental class of non-Hermitian random matrices with independently distributed complex (or real/quaternion) Gaussian entries, widely studied for its rich eigenvalue statistics in random matrix theory.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Ginibre ensemble
linked to: Ginibre ensemble
linked to: Ginibre ensemble