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Type of number sequence
In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling
Equidistributed_sequence
Number with all digits equally frequent
base b if and only if the sequence ( b k x ) k = 0 ∞ {\displaystyle {\left(b^{k}x\right)}_{k=0}^{\infty }} is equidistributed modulo 1, or equivalently
Normal_number
Type of mathematical sequence
on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice
Low-discrepancy_sequence
Mathematical sequence
multiples of an irrational α, 0, α, 2α, 3α, 4α, ... is equidistributed modulo 1. In other words, the sequence of the fractional parts of each term will be uniformly
Weyl_sequence
Topics referred to by the same term
distribution Discrete uniform distribution Uniform distribution (ecology) Equidistributed sequence All pages with titles containing uniform distribution Homogeneous
Uniform_distribution
Excess of a non-negative real number beyond its integer part
the reciprocal of its fractional part, and so on. Circle group Equidistributed sequence One-parameter group Pisot–Vijayaraghavan number Poussin proof Significand
Fractional_part
Topics referred to by the same term
Weyl's criterion may refer to: Equidistributed sequence#Weyl's criterion in uniform distribution theory Essential spectrum#Weyl's criterion in spectral
Weyl's_criterion
Class of sequences of natural numbers
distributed, equidistributed in residue classes, and even in smooth Bohr neighbourhoods. Erdős also showed that, for any particular infinite Sidon sequence A {\displaystyle
Sidon_sequence
Concept in number theory
and the upper density is 5/9. (See Benford's law.) Consider an equidistributed sequence { α n } n ∈ N {\displaystyle \{\alpha _{n}\}_{n\in \mathbb {N}
Natural_density
One-dimensional low-discrepancy sequence
exists a subsequence of the van der Corput sequence that converges to that number. They are also equidistributed over the unit interval. def corput(n, base:
Van_der_Corput_sequence
Algorithm that generates an approximation of a random number sequence
a period of 219 937 − 1 iterations (≈ 4.3×106001), is proven to be equidistributed in (up to) 623 dimensions (for 32-bit values), and at the time of its
Pseudorandom_number_generator
Theorem about Diophantine approximations
uniform by the equidistribution theorem. Weyl's criterion for equidistributed sequences Dirichlet's approximation theorem Kronecker, L. (1884), "Näherungsweise
Kronecker's_theorem
Pseudorandom number generator
equidistribution property of v-bit accuracy than MT but worse than WELL ("Well Equidistributed Long-period Linear"). It has quicker recovery from zero-excess initial
Mersenne_Twister
Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling
List of random number generators
List_of_random_number_generators
Class of pseudorandom number generators
xorshift128 generator is 2-dimensionally equidistributed, the xorshift128+ generator is only 1-dimensionally equidistributed. XSadd has some weakness in the low-order
Xorshift
Integer multiples of any irrational mod 1 are uniformly distributed on the circle
1933, proved that the generalization x + na, for almost all x, is equidistributed on any Lebesgue measurable subset of the unit interval. The corresponding
Equidistribution_theorem
Bounds of a sequence
\infty }x_{n}=+1.} (This is because the sequence { 1 , 2 , 3 , … } {\displaystyle \{1,2,3,\ldots \}} is equidistributed mod 2π, a consequence of the equidistribution
Limit inferior and limit superior
Limit_inferior_and_limit_superior
and hence random variables. It is also useful in the study of equidistributed sequences, for example in the Weyl equidistribution estimate. Loosely stated
Van_der_Corput_inequality
Halting probability of a random computer program
consequence, it is a normal number, which means that its digits are equidistributed as if they were generated by tossing a fair coin. It is not a computable
Chaitin's_constant
Algorithm for generating pseudo-randomized numbers
Nishimura, Takuji (January 1998). "Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator" (PDF). ACM Transactions on
Linear_congruential_generator
Number divisible only by 1 and itself
Makoto; Nishimura, Takuji (1998). "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator". ACM Transactions on Modeling
Prime_number
Argentine-American mathematician
Chaitin defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the
Gregory_Chaitin
Japanese Mathematician and inventor of a pseudo-random number generator
Nishimura, Takuji (January 1998). "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling
Makoto Matsumoto (mathematician)
Makoto_Matsumoto_(mathematician)
Method for generating sequences of random integers
procedure is that the period is a multiple of b, so the output is exactly equidistributed mod b. (The ordinary MWC, over its full period, produces each possible
Multiply-with-carry pseudorandom number generator
Multiply-with-carry_pseudorandom_number_generator
Hungarian and American mathematician and physicist (1903–1957)
for any dense sequence of points in [ 0 , 1 ] {\displaystyle [0,1]} , there existed a rearrangement of those points that is equidistributed. In 1926 his
John_von_Neumann
Type of mathematical group
Verdière, and Steven Zelditch states that on average, eigenfunctions equidistribute on S {\displaystyle S} . The unique quantum ergodicity conjecture of
Arithmetic_Fuchsian_group
Lie group of complex numbers of unit modulus; topologically a circle
have? For instance, is it dense in the group? Is the orbit of a point equidistributed? What is the effect of averaging functions on the circle over many
Circle_group
Generalized Inversive Congruential Pseudorandom Numbers are well equidistributed in one dimension. A reliable theoretical approach for assessing their
Generalized inversive congruential pseudorandom numbers
Generalized_inversive_congruential_pseudorandom_numbers
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