In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling...

on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice...

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...

distribution Discrete uniform distribution Uniform distribution (ecology) Equidistributed sequence All pages with titles containing uniform distribution Homogeneous...

the reciprocal of its fractional part, and so on. Circle group Equidistributed sequence One-parameter group Pisot–Vijayaraghavan number Poussin proof Significand...

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...

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}...

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...

xorshift128 generator is 2-dimensionally equidistributed, the xorshift128+ generator is only 1-dimensionally equidistributed. XSadd has some weakness in the low-order...

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...

exists a subsequence of the van der Corput sequence that converges to that number. They are also equidistributed over the unit interval. double corput(int...

elements of the torus) converges. In particular, this sequence is not equidistributed mod 1. The lower powers of the silver ratio are δ S − 1 = 1 δ S − 2...

and hence random variables. It is also useful in the study of equidistributed sequences, for example in the Weyl equidistribution estimate. Loosely stated...

1933, proved that the generalization x + na, for almost all x, is equidistributed on any Lebesgue measurable subset of the unit interval. The corresponding...

\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...

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 has defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the...

Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling...

"Middle-Square Weyl Sequence RNG". arXiv:1704.00358 [cs.CR]. Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A 623-dimensionally Equidistributed Uniform Pseudo-Random...

Nishimura, Takuji (January 1998). "Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator" (PDF). ACM Transactions on...

Nishimura, Takuji (January 1998). "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling...

Makoto; Nishimura, Takuji (1998). "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator". ACM Transactions on Modeling...

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...

Generalized Inversive Congruential Pseudorandom Numbers are well equidistributed in one dimension. A reliable theoretical approach for assessing their...

Colin de Verdière and Zelditch states that on average, eigenfunctions equidistribute on S {\displaystyle S} . The unique quantum ergodicity conjecture of...