jointEigenvalueDensity
P128209
predicate
Indicates the relationship that assigns a probability density to each possible combination of eigenvalues considered jointly, rather than individually.
All labels observed (6)
| Label | Occurrences |
|---|---|
| eigenvalueDistribution | 1 |
| eigenvalueJointDensity | 1 |
| hasEigenvalueDistribution | 1 |
| hasJointEigenvalueDensity | 1 |
| hasJointEigenvalueDensityProportionalTo | 1 |
| jointEigenvalueDensity canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: jointEigenvalueDensity
Generated description
Indicates the relationship that assigns a probability density to each possible combination of eigenvalues considered jointly, rather than individually.
Sample triples (6)
| Subject | Object |
|---|---|
| Gaussian orthogonal ensemble | given by Vandermonde determinant to the first power times Gaussian weight ⓘ |
| Gaussian unitary ensemble | determinantal point process via predicate surface "eigenvalueDistribution" ⓘ |
| Gaussian unitary ensemble | proportional to exp(-Σ λ_i^2/2σ^2) Π_{i<j}(λ_i-λ_j)^2 via predicate surface "eigenvalueJointDensity" ⓘ |
| Gaussian symplectic ensemble | proportional to exp(- (β/2) Σ λ_i^2 ) ∏_{i<j} |λ_i - λ_j|^β with β = 4 via predicate surface "hasJointEigenvalueDensity" ⓘ |
| Jacobi ensemble | joint density supported on a compact interval via predicate surface "hasEigenvalueDistribution" ⓘ |
| Jacobi ensemble | ∏_{i<j} |λ_i-λ_j|^β ∏_{i} λ_i^{α} (1-λ_i)^{γ} via predicate surface "hasJointEigenvalueDensityProportionalTo" ⓘ |