In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carlo integration.
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In mathematics, a sequence (s1, s2, s3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling...
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) Equidistributedsequence All pages with titles containing uniform distribution Homogeneous...
the reciprocal of its fractional part, and so on. Circle group Equidistributedsequence One-parameter group Pisot–Vijayaraghavan number Significand "Decimal...
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 equidistributedsequence { 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...
and hence random variables. It is also useful in the study of equidistributedsequences, 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...
Matsumoto, M.; Nishimura, T. (1998). "MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator". ACM Transactions on Modeling...
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...
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...
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...
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