Erdős–Rényi law of large numbers
E554306
The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Erdős–Rényi law of large numbers canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5896714 — 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: Erdős–Rényi law of large numbers Context triple: [Pál Erdős, knownFor, Erdős–Rényi law of large numbers]
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A.
Khinchin's law of the iterated logarithm
Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
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B.
law of large numbers
The law of large numbers is a fundamental theorem in probability theory stating that as the number of independent trials increases, the sample average converges to the expected value.
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C.
Limit Laws for Sums of Independent Random Variables
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
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D.
Erdős–Rényi model
The Erdős–Rényi model is a fundamental random graph model in probability theory and network science, where edges between pairs of nodes are included independently with a fixed probability.
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E.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
- 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: Erdős–Rényi law of large numbers Target entity description: The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
-
A.
Khinchin's law of the iterated logarithm
Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
-
B.
law of large numbers
The law of large numbers is a fundamental theorem in probability theory stating that as the number of independent trials increases, the sample average converges to the expected value.
-
C.
Limit Laws for Sums of Independent Random Variables
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
-
D.
Erdős–Rényi model
The Erdős–Rényi model is a fundamental random graph model in probability theory and network science, where edges between pairs of nodes are included independently with a fixed probability.
-
E.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
probability theorem
ⓘ
refinement of the law of large numbers ⓘ result in probability theory ⓘ |
| appliesTo |
identically distributed random variables
ⓘ
independent random variables ⓘ |
| assumes |
finite variance under common formulations
ⓘ
independence of summands ⓘ |
| characterizes | fluctuations of normalized partial sums ⓘ |
| concerns |
almost sure convergence
ⓘ
behavior of partial sums on logarithmic scales ⓘ rate of almost sure convergence ⓘ |
| describes |
asymptotic behavior of sums of independent random variables
ⓘ
precise convergence rates in the law of large numbers ⓘ |
| developedBy |
Alfréd Rényi
ⓘ
Pál Erdős ⓘ |
| era | 20th century mathematics ⓘ |
| field |
mathematical statistics
ⓘ
probability theory ⓘ |
| focusesOn | fine asymptotics beyond classical LLN ⓘ |
| hasConcept |
almost sure growth rate of partial sums
ⓘ
normalization of sums by slowly varying functions ⓘ |
| influenced | subsequent work on precise asymptotics in probability ⓘ |
| language | mathematical notation ⓘ |
| mathematicalDomain | measure-theoretic probability ⓘ |
| namedAfter |
Alfréd Rényi
ⓘ
Pál Erdős ⓘ |
| provides |
logarithmic normalization for partial sums
ⓘ
precise asymptotic bounds for partial sums ⓘ |
| refines |
classical law of large numbers
ⓘ
strong law of large numbers ⓘ |
| relatedTo |
Kolmogorov strong law of large numbers
ⓘ
large deviations theory ⓘ law of the iterated logarithm ⓘ
linked to:
Kolmogorov's law of the iterated logarithm
|
| topicOf | research in asymptotic probability ⓘ |
| typeOf |
almost sure limit theorem
ⓘ
limit theorem ⓘ |
| usedIn |
limit theorems for sums of random variables
ⓘ
theoretical probability ⓘ |
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: Erdős–Rényi law of large numbers Description of subject: The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.