Poisson distribution has P(s) = e^{-s}
E443155
The Poisson distribution with P(s) = e^{-s} is a simple statistical model describing uncorrelated, randomly spaced events, often used as a reference for comparison in random matrix theory and spectral statistics.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Poisson distribution with P(s) = e^{-s} | 0 |
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
probability distribution
ⓘ
reference model in spectral statistics ⓘ statistical model ⓘ |
| arisesFrom | Poisson point process on the line with unit intensity ⓘ |
| associatedWith |
integrable quantum systems
ⓘ
uncorrelated spectra ⓘ |
| assumes | absence of level repulsion ⓘ |
| belongsToFamily | exponential family ⓘ |
| characterizes | spectra of many-body localized phases (idealized) ⓘ |
| comparedWith |
Gaussian orthogonal ensemble spacing distribution
NERFINISHED
ⓘ
Gaussian symplectic ensemble spacing distribution ⓘ Gaussian unitary ensemble spacing distribution NERFINISHED ⓘ |
| contrastedWith | Wigner–Dyson level spacing distributions NERFINISHED ⓘ |
| describes | uncorrelated randomly spaced events ⓘ |
| hasCumulativeDistributionFunction | F(s) = 1 - e^{-s} ⓘ |
| hasHazardRate | 1 ⓘ |
| hasMeanSpacing | 1 ⓘ |
| hasMedian | ln(2) ⓘ |
| hasMode | 0 ⓘ |
| hasProbabilityDensityFunction | P(s) = e^{-s} ⓘ |
| hasSupport | s ≥ 0 ⓘ |
| hasVariance | 1 ⓘ |
| implies | finite probability of very small spacings ⓘ |
| indicates | lack of correlations between levels ⓘ |
| isContinuous | true ⓘ |
| isExponentialDistribution | true ⓘ |
| isLimitingCaseOf | Poisson process inter-arrival time distribution with λ = 1 ⓘ |
| isMemoryless | true ⓘ |
| isOneDimensional | true ⓘ |
| models | level spacing statistics of uncorrelated energy levels ⓘ |
| parameter | rate λ = 1 ⓘ |
| usedAs | reference for comparison with non-Poissonian spectra ⓘ |
| usedAsBenchmark | for detecting level repulsion ⓘ |
| usedAsNullHypothesisFor | tests of spectral correlations ⓘ |
| usedIn |
analysis of integrable vs chaotic spectra
ⓘ
quantum chaos diagnostics ⓘ random matrix theory ⓘ spectral statistics ⓘ |
| usedToModel |
uncorrelated eigenvalue spacings
ⓘ
uncorrelated event times ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.