Erdős–Rényi law of large numbers
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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 |
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
NERFINISHED
ⓘ
Pál Erdős NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
Pál Erdős NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
large deviations theory ⓘ law of the iterated logarithm NERFINISHED ⓘ |
| topicOf | research in asymptotic probability ⓘ |
| typeOf |
almost sure limit theorem
ⓘ
limit theorem ⓘ |
| usedIn |
limit theorems for sums of random variables
ⓘ
theoretical probability ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.