Gaussian β-ensembles
E1284828
UNEXPLORED
Gaussian β-ensembles are families of random matrix models in which eigenvalue statistics depend continuously on a parameter β that governs the strength of eigenvalue repulsion and interpolates between classical matrix ensembles.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gaussian β-ensembles canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T17752890 — 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 β-ensembles Context triple: [Dyson index β, usedToLabel, Gaussian β-ensembles]
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A.
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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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.
Wigner matrices
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.
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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.
Wigner semicircle law
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.
- 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 β-ensembles Target entity description: Gaussian β-ensembles are families of random matrix models in which eigenvalue statistics depend continuously on a parameter β that governs the strength of eigenvalue repulsion and interpolates between classical matrix ensembles.
-
A.
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.
-
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.
Wigner matrices
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.
-
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.
Wigner semicircle law
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.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.