the iterated logarithm of n {\displaystyle n} , written log*  n {\displaystyle n} (usually read "log star"), is the number of times the logarithm function...

the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due...

include the double logarithm ln(ln(x)), the super- or hyper-4-logarithm (a slight variation of which is called iterated logarithm in computer science)...

iterated exponentials, as it is common to call expressions of this form iterated exponentiation, which is ambiguous, as this can either mean iterated...

definition of an iterated function on a set X follows. Let X be a set and f: X → X be a function. Defining f n as the n-th iterate of f, where n is a...

In mathematics, the Wiener process (or Brownian motion, due to its historical connection with the physical process of the same name) is a real-valued continuous-time...

Superposition of the previous three graphs Iterated logarithm Napierian logarithm List of logarithmic identities Logarithm of a matrix Logarithmic coordinates...

series History of logarithms Hyperbolic sector Iterated logarithm Otis King Law of the iterated logarithm Linear form in logarithms Linearithmic List...

relative error between their logarithms is still large; however, the relative error in their second-iterated logarithms is small: log 10 ⁡ ( log 10 ⁡...

functions Meijer G-function Fox H-function Hyper operators Iterated logarithm Pentation Super-logarithms Tetration Lambert W function: Inverse of f(w) = w exp(w)...

paper An Invariance Principle for the Law of the Iterated Logarithm. Strassen's law of the iterated logarithm has been widely cited and led to a 1966 presentation...

founders of modern probability theory, discovering the law of the iterated logarithm in 1924, achieving important results in the field of limit theorems...

also be multiplied by a slowly varying function of n. The law of the iterated logarithm specifies what is happening "in between" the law of large numbers...

bounded to O ( log ∗ ⁡ ( n ) ) {\displaystyle O(\log ^{*}(n))} , the iterated logarithm of n {\displaystyle n} , by Hopcroft and Ullman. In 1975, Robert Tarjan...

2005), and every graph whose average degree is exponential in the iterated logarithm of n necessarily contains a cycle whose length is a power of two (Sudakov...

constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after...

Cajori, Florian (1952) [March 1929]. "§472. The power of a logarithm / §473. Iterated logarithms / §533. John Herschel's notation for inverse functions /...

binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the...

chance of landing on 2. The central limit theorem and the law of the iterated logarithm describe important aspects of the behavior of simple random walks...

Cajori, Florian (1952) [March 1929]. "§472. The power of a logarithm / §473. Iterated logarithms / §533. John Herschel's notation for inverse functions /...

theorem Keynes' Treatise on Probability Law of averages Law of the iterated logarithm Law of truly large numbers Lindy effect Regression toward the mean...

the form of F. Another result, which follows from the law of the iterated logarithm, is that lim sup n → ∞ n ‖ F ^ n − F ‖ ∞ 2 ln ⁡ ln ⁡ n ≤ 1 2 , a.s...

(assuming that we have unique node identifiers). The function log*, iterated logarithm, is an extremely slowly growing function, "almost constant". Hence...

where the number of terms in the sum is bounded above by the binary iterated logarithm. To be precise, let f ( x ) = ⌊ log 2 ⁡ x ⌋ {\displaystyle f(x)=\lfloor...

method to send the iterates outside of the domain, so that it is impossible to continue the iteration. For example, the natural logarithm function f(x) =...

number is proportional to its logarithm; therefore, the additive persistence is proportional to the iterated logarithm. The example below implements the...

^{*}n}}))} by Santhanam, where log ∗ ⁡ n {\displaystyle \log ^{*}n} is the iterated logarithm. If we use an alternating Turing machine, we have the resource ATIME...

statements for x t {\displaystyle x_{t}} . For instance, the law of the iterated logarithm for W t {\displaystyle W_{t}} becomes lim sup t → ∞ x t ( σ 2 / θ...

^{*}n+\log k)} ; here log ∗ ⁡ n {\displaystyle \log ^{*}n} is the iterated logarithm. For a collection of data values undergoing dynamic insertions and...

at most proportional to its logarithm; therefore, the additive persistence is at most proportional to the iterated logarithm, and the smallest number of...