Dyson index β
E443154
The Dyson index β is a parameter in random matrix theory that classifies ensembles by their underlying symmetry, typically taking values 1, 2, or 4 for orthogonal, unitary, and symplectic ensembles, respectively.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Dyson index β canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4461554 — 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: Dyson index β Context triple: [Wigner surmise, parameter, Dyson index β]
-
A.
Dyson series
The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
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B.
Dyson tree concept
The Dyson tree concept is a speculative astroengineering idea proposing genetically engineered, space-adapted trees that could grow on comets or small bodies to create habitable environments in space.
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C.
Dyson’s formula
Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
-
D.
Dyson shell
A Dyson shell is a hypothetical megastructure consisting of a vast swarm or continuous layer of objects surrounding a star to capture a significant portion of its energy output.
-
E.
Huber-Dyson
Huber-Dyson is the surname of Verena Huber-Dyson, a Swiss-American mathematician and logician known for her work in group theory and the foundations of mathematics.
- 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: Dyson index β Target entity description: The Dyson index β is a parameter in random matrix theory that classifies ensembles by their underlying symmetry, typically taking values 1, 2, or 4 for orthogonal, unitary, and symplectic ensembles, respectively.
-
A.
Dyson series
The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
-
B.
Dyson tree concept
The Dyson tree concept is a speculative astroengineering idea proposing genetically engineered, space-adapted trees that could grow on comets or small bodies to create habitable environments in space.
-
C.
Dyson’s formula
Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
-
D.
Dyson shell
A Dyson shell is a hypothetical megastructure consisting of a vast swarm or continuous layer of objects surrounding a star to capture a significant portion of its energy output.
-
E.
Huber-Dyson
Huber-Dyson is the surname of Verena Huber-Dyson, a Swiss-American mathematician and logician known for her work in group theory and the foundations of mathematics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Dyson symmetry class parameter
ⓘ
parameter in random matrix theory ⓘ symmetry index ⓘ |
| appearsIn |
Vandermonde determinant exponent
ⓘ
Wigner–Dyson statistics NERFINISHED ⓘ joint eigenvalue distribution ⓘ |
| canTake | positive real values in generalized β-ensembles ⓘ |
| classifies |
Gaussian ensembles
NERFINISHED
ⓘ
circular ensembles ⓘ random matrix ensembles ⓘ |
| classifiesBy | underlying symmetry ⓘ |
| controls | level repulsion exponent ⓘ |
| determines |
short-range spectral correlations
ⓘ
spacing distribution between eigenvalues ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ spectral theory ⓘ |
| generalizationOf | Wigner’s symmetry classification NERFINISHED ⓘ |
| introducedInContextOf | Dyson’s threefold way NERFINISHED ⓘ |
| mathematicalRole | exponent in eigenvalue interaction term ⓘ |
| namedAfter | Freeman Dyson NERFINISHED ⓘ |
| relatedTo |
spin-rotation symmetry
ⓘ
time-reversal symmetry ⓘ universality classes in random matrix theory ⓘ |
| takesTypicalValue |
1
ⓘ
2 ⓘ 4 ⓘ |
| usedIn |
mesoscopic physics
ⓘ
nuclear physics ⓘ number theory ⓘ quantum chaos ⓘ random matrix theory NERFINISHED ⓘ |
| usedToLabel |
Gaussian β-ensembles
NERFINISHED
ⓘ
Jacobi β-ensembles NERFINISHED ⓘ Laguerre β-ensembles NERFINISHED ⓘ |
| value1AssociatedWith |
Gaussian orthogonal ensemble
NERFINISHED
ⓘ
circular orthogonal ensemble ⓘ |
| value1CorrespondsTo | orthogonal symmetry ⓘ |
| value2AssociatedWith |
Gaussian unitary ensemble
NERFINISHED
ⓘ
circular unitary ensemble ⓘ |
| value2CorrespondsTo | unitary symmetry ⓘ |
| value4AssociatedWith |
Gaussian symplectic ensemble
NERFINISHED
ⓘ
circular symplectic ensemble ⓘ |
| value4CorrespondsTo | symplectic symmetry ⓘ |
| βEquals1Implies | presence of time-reversal symmetry and integer spin ⓘ |
| βEquals2Implies | absence of time-reversal symmetry ⓘ |
| βEquals4Implies | presence of time-reversal symmetry with half-integer spin ⓘ |
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: Dyson index β Description of subject: The Dyson index β is a parameter in random matrix theory that classifies ensembles by their underlying symmetry, typically taking values 1, 2, or 4 for orthogonal, unitary, and symplectic ensembles, respectively.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.