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.
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 NERFINISHED ⓘ Selberg integral NERFINISHED ⓘ 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
NERFINISHED
ⓘ
logarithm of eigenvalue differences ⓘ squared Vandermonde determinant ⓘ |
| mathematicalField |
analysis
ⓘ
mathematical physics ⓘ probability theory ⓘ |
| namedAfter | Freeman Dyson NERFINISHED ⓘ |
| relatedTo |
Coulomb gas
NERFINISHED
ⓘ
Dyson gas ⓘ Gaussian Orthogonal Ensemble NERFINISHED ⓘ Gaussian Symplectic Ensemble NERFINISHED ⓘ Gaussian Unitary Ensemble NERFINISHED ⓘ 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 ⓘ |
Referenced by (1)
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