The MIXMAX random number generator

@article{Savvidy2015TheMR,
  title={The MIXMAX random number generator},
  author={Konstantin G. Savvidy},
  journal={Comput. Phys. Commun.},
  year={2015},
  volume={196},
  pages={161-165}
}
  • K. Savvidy
  • Published 2015
  • Mathematics, Computer Science, Physics
  • Comput. Phys. Commun.
Abstract In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50… Expand
Spectral Analysis of the MIXMAX Random Number Generators
TLDR
It is shown that for coordinates at specific lags not too far apart, in three dimensions, all the nonzero points lie in only two hyperplanes, reminiscent of the behavior of lagged-Fibonacci and AWC/SWB generators. Expand
Classical limit theorems and high entropy MIXMAX random number generator
We investigate the interrelation between the distribution of stochastic fluctuations of independent random variables in probability theory and the distribution of time averages in deterministicExpand
A Priori Tests for the MIXMAX Random Number Generator
We define two a priori tests of pseudo-random number generators for the class of linear matrix-recursions. The first desirable property of a random number generator is the smallness of serial orExpand
Spectral test of the MIXMAX random number generators
Abstract An important statistical test on the pseudo-random number generators is called the spectral test. The test is aimed at answering the question of distribution of the generated pseudo-randomExpand
Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers
Abstract We are developing further our earlier suggestion to use high entropy Anosov C-systems for the Monte-Carlo simulations. The hyperbolic Anosov C-systems have exponential instability of theirExpand
Review of High-Quality Random Number Generators
TLDR
This paper outlines the Kolmogorov–Anosov theory of mixing in classical mechanical systems, and establishes criteria for deciding which RNG’s are sufficiently good approximations to the ideal mathematical systems that guarantee highest quality. Expand
Spectrum and entropy of C-systems MIXMAX random number generator
Abstract The uniformly hyperbolic Anosov C-systems defined on a torus have very strong instability of their trajectories, as strong as it can be in principle. These systems have exponentialExpand
Anosov C-systems and random number generators
We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics.Expand
A new Pseudo random number generator based on generalized Newton complex map with dynamic key
TLDR
A new generalized map based on Newton complex map is proposed that is capable of generating pseudo random numbers in both integer and complex domain, and it can be used in hardware implementations due to its low dimension. Expand
Distribution of periodic trajectories of C-K systems MIXMAX pseudorandom number generator
We are considering the hyperbolic C-K systems of Anosov–Kolmogorov which are defined on high dimensional tori and are used to generate pseudorandom numbers for Monte-Carlo simulations. AllExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 35 REFERENCES
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
TLDR
A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers, which provides a super astronomical period of 2 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. Expand
Deterministic Simulation of Random Processes
and the sciences we are required to simulate random processes. The simulation is usually effected by a computer program which generates a non-random, deterministic sequence of numbers xl, x2, I *Expand
K-System Generator of Pseudorandom Numbers on Galois Field
We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on a rational sublattice which coincides with the Galois field GF[p]. The period of theExpand
Random numbers fall mainly in the planes.
  • G. Marsaglia
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1968
TLDR
The paper gives details of the degree of regularity of congruential random number generators in terms of sets of relatively few parallel hyperplanes which contain all of the points produced by the generator. Expand
Matrix generators for pseudo-random vector generation
In this paper a method for the direct generation of pseudo-random vectors is considered. Thereby the n-th pseudo-random vector is recursively generated from the (n−1)-th pseudo-random vector byExpand
The RANLUX Generator: Resonances in a Random Walk Test
Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Luscher and implemented by James. We confirm the goodExpand
RANLUX: A Fortran implementation of the high-quality pseudorandom number generator of Lüscher
TLDR
A portable Fortran 77 implementation of a high-quality generator called RANLUX (for LUXury RANdom numbers), using the algorithm of Martin Luscher described in an accompanying article. Expand
A portable high-quality random number generator for lattice field theory simulations
Abstract The theory underlying a proposed random number generator for numerical simulations in elementary particle physics and statistical mechanics is discussed. The generator is based on anExpand
Equidistribution of Matrix-Power Residues Modulo One
Here {y\ = y — [y] = the fractional part of y. The number N is an integer >1. The number x0 is a given initial value such that 0 ^ Xo < 1. The number 0 is fixed. Some early references to numericalExpand
FINITE FIELDS
This handout discusses finite fields: how to construct them, properties of elements in a finite field, and relations between different finite fields. We write Z/(p) and Fp interchangeably for theExpand
...
1
2
3
4
...