Dyson integral
E865109
The Dyson integral is a multidimensional integral arising in random matrix theory and statistical physics that evaluates averages over eigenvalue distributions with logarithmic interactions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Dyson integral canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10462106 — 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 integral Context triple: [Selberg integral, relatedTo, Dyson integral]
-
A.
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.
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B.
Poisson integral
The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
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C.
Dyson index β
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.
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D.
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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E.
Fresnel integrals
Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
- 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 integral Target entity description: The Dyson integral is a multidimensional integral arising in random matrix theory and statistical physics that evaluates averages over eigenvalue distributions with logarithmic interactions.
-
A.
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.
-
B.
Poisson integral
The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
-
C.
Dyson index β
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.
-
D.
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.
-
E.
Fresnel integrals
Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical integral
ⓘ
object in random matrix theory ⓘ object in statistical physics ⓘ |
| arisesIn |
random matrix theory
ⓘ
statistical physics ⓘ |
| associatedWith |
Dyson index beta
ⓘ
orthogonal invariance ⓘ symplectic invariance ⓘ unitary invariance ⓘ |
| connectedTo |
Coulomb gas method
ⓘ
Mehta integral ⓘ Selberg integral ⓘ orthogonal polynomials ⓘ |
| dependsOn |
confining potential
ⓘ
interaction strength beta ⓘ |
| hasApplication |
condensed matter physics
ⓘ
nuclear physics ⓘ number theory models ⓘ quantum transport ⓘ |
| hasDomain | eigenvalue space ⓘ |
| hasInteractionType | logarithmic interactions ⓘ |
| hasParameter |
inverse temperature beta
ⓘ
matrix size N ⓘ |
| hasRole |
generating function for eigenvalue correlations
ⓘ
normalization constant of random matrix ensembles ⓘ |
| integrandInvolves |
Vandermonde determinant
ⓘ
linked to:
Vandermonde matrix
logarithm of eigenvalue differences ⓘ squared Vandermonde determinant ⓘ |
| mathematicalField |
analysis
ⓘ
mathematical physics ⓘ probability theory ⓘ |
| namedAfter | Freeman Dyson ⓘ |
| relatedTo |
Coulomb gas
ⓘ
Dyson gas ⓘ Gaussian Orthogonal Ensemble ⓘ
linked to:
Gaussian orthogonal ensemble
Gaussian Symplectic Ensemble ⓘ
linked to:
Gaussian symplectic ensemble
Gaussian Unitary Ensemble ⓘ
linked to:
Gaussian unitary ensemble
beta-ensembles ⓘ log-gas model ⓘ random matrix eigenvalue statistics ⓘ |
| usedFor |
averages over eigenvalue distributions
ⓘ
computation of correlation functions ⓘ evaluation of partition functions ⓘ |
| usedIn |
spectral statistics of complex quantum systems
ⓘ
statistical mechanics of eigenvalues ⓘ theory of quantum chaos ⓘ |
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 integral Description of subject: The Dyson integral is a multidimensional integral arising in random matrix theory and statistical physics that evaluates averages over eigenvalue distributions with logarithmic interactions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.