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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Poisson distribution has P(s) = e^{-s} canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4461570 — 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: Poisson distribution has P(s) = e^{-s}
Context triple: [Wigner surmise, PoissonComparison, Poisson distribution has P(s) = e^{-s}]
-
A.
Pareto distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
-
B.
Khinchin–Pollaczek formula
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
-
C.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
-
D.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
E.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
- 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: Poisson distribution has P(s) = e^{-s}
Target entity description: 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.
-
A.
Pareto distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
-
B.
Khinchin–Pollaczek formula
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
-
C.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
-
D.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
E.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
- F. None of above. chosen
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 ⓘ |
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: Poisson distribution has P(s) = e^{-s}
Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.