Khinchin–Kahane type inequalities
E87730
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Kahane inequality | 1 |
| Khinchin inequality | 1 |
| Khinchin–Kahane type inequalities canonical | 1 |
| Khintchine inequality | 1 |
| noncommutative Khinchin–Kahane inequalities | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T736603 — 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.
Target entity: Khinchin–Kahane type inequalities Context triple: [Minkowski inequality, isSpecialCaseOf, Khinchin–Kahane type inequalities]
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A.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
B.
Minkowski inequality
The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Cameron–Martin theorem
The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
-
E.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Khinchin–Kahane type inequalities Target entity description: Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
-
A.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
B.
Minkowski inequality
The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Cameron–Martin theorem
The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
-
E.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
functional analysis result
ⓘ
moment inequality ⓘ norm inequality ⓘ probability inequality ⓘ |
| appliesTo |
Gaussian series
ⓘ
Rademacher series ⓘ series with independent symmetric coefficients ⓘ |
| assumes |
independence of random signs or coefficients
ⓘ
symmetry of random signs in classical form ⓘ |
| field |
Banach space theory
ⓘ
functional analysis ⓘ probability theory ⓘ random processes ⓘ |
| generalizes |
Khinchin–Kahane type inequalities
self-linksurface differs
ⓘ
surface form:
Kahane inequality
Khinchin–Kahane type inequalities self-linksurface differs ⓘ
surface form:
Khinchin inequality
|
| hasProperty |
constants depend on p but not on number of terms
ⓘ
dimension-free constants in many formulations ⓘ |
| hasVariant |
Khinchin–Kahane type inequalities
self-linksurface differs
ⓘ
surface form:
noncommutative Khinchin–Kahane inequalities
subgaussian Khinchin–Kahane inequalities ⓘ vector-valued Khinchin–Kahane inequalities ⓘ |
| implies | stability of random series under change of p-norm ⓘ |
| namedAfter |
Aleksandr Khinchin
ⓘ
Jean-Pierre Kahane ⓘ |
| provides |
bounds between different moments
ⓘ
bounds between different norms ⓘ |
| relatedTo |
Littlewood–Paley theory
ⓘ
cotype of a Banach space ⓘ type of a Banach space ⓘ unconditional convergence of random series ⓘ vector-valued Khinchin inequalities ⓘ |
| relates |
L2 norm and Lp norms
ⓘ
Lp norms of random series ⓘ moments of random series ⓘ |
| typicalForm |
equivalence of Lp norms of Rademacher series for 0<p<∞
ⓘ
two-sided bounds between Lp and Lq norms of random series ⓘ |
| usedFor |
analysis of vector-valued random variables
ⓘ
bounding tail behavior of random sums ⓘ comparison of Lp norms for random series ⓘ studying geometry of Banach spaces ⓘ studying random series in Banach spaces ⓘ studying type and cotype of Banach spaces ⓘ |
| usedIn |
analysis of random Fourier series
ⓘ
asymptotic geometric analysis ⓘ high-dimensional probability ⓘ study of empirical processes ⓘ |
| usesRandomVariables |
Gaussian random variables
ⓘ
Rademacher random variables ⓘ |
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Subject: Khinchin–Kahane type inequalities Description of subject: Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.