BBP phase transition
E898469
The BBP phase transition is a phenomenon in random matrix theory describing the critical point at which an eigenvalue associated with a low-rank perturbation separates from the bulk spectrum, leading to a detectable “spike.”
All labels observed (1)
| Label | Occurrences |
|---|---|
| BBP phase transition canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991215 — 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: BBP phase transition Context triple: [random matrix theory, hasKeyConcept, BBP phase transition]
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A.
BBPR
BBPR was an influential 20th-century Italian architectural and design collective known for its modernist and rationalist works, including major postwar projects in Italy.
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B.
BPPC
BPPC (Basic Patient Privacy Consents) is an IHE IT Infrastructure profile that defines how healthcare systems capture, manage, and enforce patients’ privacy consent directives in electronic health information exchange.
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C.
Peierls transition
The Peierls transition is a phase transition in one-dimensional metals where a periodic lattice distortion opens an energy gap at the Fermi surface, turning the system from a metal into an insulator or semiconductor.
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D.
BBR
BBR is the common abbreviation for Basketball-Reference.com, a comprehensive online database of basketball statistics and historical player and team information.
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E.
.bb
.bb is the country code top-level domain (ccTLD) assigned to Barbados for use in internet addresses associated with the country.
- 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: BBP phase transition Target entity description: The BBP phase transition is a phenomenon in random matrix theory describing the critical point at which an eigenvalue associated with a low-rank perturbation separates from the bulk spectrum, leading to a detectable “spike.”
-
A.
BBPR
BBPR was an influential 20th-century Italian architectural and design collective known for its modernist and rationalist works, including major postwar projects in Italy.
-
B.
BPPC
BPPC (Basic Patient Privacy Consents) is an IHE IT Infrastructure profile that defines how healthcare systems capture, manage, and enforce patients’ privacy consent directives in electronic health information exchange.
-
C.
Peierls transition
The Peierls transition is a phase transition in one-dimensional metals where a periodic lattice distortion opens an energy gap at the Fermi surface, turning the system from a metal into an insulator or semiconductor.
-
D.
BBR
BBR is the common abbreviation for Basketball-Reference.com, a comprehensive online database of basketball statistics and historical player and team information.
-
E.
.bb
.bb is the country code top-level domain (ccTLD) assigned to Barbados for use in internet addresses associated with the country.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical phenomenon
ⓘ
phase transition in random matrix theory ⓘ |
| alsoKnownAs | Baik–Ben Arous–Péché phase transition ⓘ |
| appliesTo |
Wigner-type random matrices
ⓘ
low-rank perturbations of large random matrices ⓘ sample covariance matrices ⓘ spiked random matrix models ⓘ |
| characterizedBy |
change in eigenvector alignment with the signal direction
ⓘ
eigenvalue leaving the support of the limiting spectral distribution ⓘ transition between undetectable and detectable spikes ⓘ |
| concerns |
fluctuations of the top eigenvalue near the critical point
ⓘ
largest eigenvalue behavior under rank-one perturbations ⓘ threshold for eigenvalue separation from the bulk ⓘ |
| describes |
critical point where an eigenvalue separates from the bulk spectrum
ⓘ
detectability threshold for a spike in spiked random matrix models ⓘ emergence of an outlier eigenvalue due to low-rank perturbation ⓘ |
| field |
mathematical statistics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| hasAspect |
critical regime with nonstandard fluctuation behavior
ⓘ
subcritical regime where spike is not detectable ⓘ supercritical regime where an outlier eigenvalue appears ⓘ |
| hasImplication |
design of optimal tests for spiked alternatives
ⓘ
fundamental detection limits in noisy matrix models ⓘ limits of PCA for weak signals in high dimensions ⓘ |
| introducedIn | paper by Baik, Ben Arous, and Péché on eigenvalues of deformed random matrices ⓘ |
| involves |
low-rank deformation of invariant random matrix ensembles
ⓘ
spectral properties of large random matrices ⓘ |
| mathematicalContext |
asymptotic regime of large matrix dimension
ⓘ
limit of eigenvalue distributions ⓘ |
| namedAfter |
Gérard Ben Arous
ⓘ
Jinho Baik ⓘ Sandrine Péché ⓘ |
| relatedTo |
Marchenko–Pastur law
ⓘ
Tracy–Widom distribution ⓘ eigenvalue outliers ⓘ phase transitions in high-dimensional statistics ⓘ principal component analysis ⓘ signal detection in high dimensions ⓘ spiked covariance model ⓘ |
| usedIn |
finance and portfolio theory
ⓘ
genomics and population genetics ⓘ high-dimensional hypothesis testing ⓘ statistical signal processing ⓘ wireless communications ⓘ |
| yearIntroduced | 2005 ⓘ |
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: BBP phase transition Description of subject: The BBP phase transition is a phenomenon in random matrix theory describing the critical point at which an eigenvalue associated with a low-rank perturbation separates from the bulk spectrum, leading to a detectable “spike.”
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.