1948. The van der Corput sequence is equidistributed. Weyl's criterion states that the sequence an is equidistributed modulo 1 if and only if for all non-zero...

) k = 0 ∞ {\displaystyle {\left(b^{k}x\right)}_{k=0}^{\infty }} is equidistributed modulo 1, or equivalently, using Weyl's criterion, if and only if lim...

sequence of all 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...

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...

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

The Well Equidistributed Long-period Linear (WELL) is a family of pseudorandom number generators developed in 2006 by François Panneton, Pierre L'Ecuyer...

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

{\displaystyle [0,1]} , there existed a rearrangement of those points that is equidistributed. In 1926 his sole publication was on Prüfer's theory of ideal algebraic...

Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-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...

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...

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

distribution is uniform by the equidistribution theorem. Weyl's criterion for equidistributed sequences Dirichlet's approximation theorem Kronecker, L. (1884), "Näherungsweise...

Weyl's criterion may refer to: Equidistributed sequence#Weyl's criterion in uniform distribution theory Essential spectrum#Weyl's criterion in spectral...

methods cannot be used, because the integrand is only given at the fixed equidistributed grid or because the integrand is not sufficiently smooth, then Runge's...

1/9 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...

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

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

example, it is known that dense Sidon sets are uniformly distributed, equidistributed in residue classes, and even in smooth Bohr neighbourhoods. Erdős also...

consistent with the intuition that the flows of ergodic systems are equidistributed in phase space. By contrast, classical completely integrable systems...

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...

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

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

with major index i and k inversions, that is, the two statistics are equidistributed. For example, the number of permutations of length 4 with given major...

1978 by Charles Matthews. In 1978 Patterson conjectured that θp was equidistributed with error term asymptotically of order X 5 6 {\displaystyle X^{\frac...

the sequence { 1 , 2 , 3 , … } {\displaystyle \{1,2,3,\ldots \}} is equidistributed mod 2π, a consequence of the equidistribution theorem.) An example...

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

Taylor, Harris and Shepherd-Barron, and says that the error terms are equidistributed. Elliptic curves over finite fields are notably applied in cryptography...

finite volume, orbits of a Zariski dense subgroup of a semisimple group equidistributed towards algebraic measures. He gave the 2012 Takagi Lectures in Kyoto...

sufficient condition for when the orbit under the absolute Galois group is equidistributed. He spent time at the Institute for Advanced Study, Princeton University...

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

Pennsylvania, United States The WELL, an online virtual community Well equidistributed long-period linear, a pseudorandom number generator Well (disambiguation)...

van der Corput sequence that converges to that number. They are also equidistributed over the unit interval. def corput(n, base: int) -> float: """ Returns...

for arithmetic progressions shows that the primes are asymptotically equidistributed among the residue classes. The Bombieri–Vinogradov theorem gives a...

curve evolutions by stable fully implicit finite element schemes that equidistribute" (PDF), Numerical Methods for Partial Differential Equations, 27: 1–30...

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...

Ratner equidistribution theorem further asserts that each such orbit is equidistributed in its closure. The Ratner measure classification theorem is the weaker...

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...

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

of works, Walter Gubler proved that Galois orbits of small points do equidistribute to this Chambert-Loir measure and studied its properties using tropical...