# 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} }

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

#### 34 Citations

Spectral Analysis of the MIXMAX Random Number Generators

- Computer Science, Mathematics
- INFORMS J. Comput.
- 2020

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

- Mathematics, Physics
- 2017

We investigate the interrelation between the distribution of stochastic fluctuations of independent random variables in probability theory and the distribution of time averages in deterministic… Expand

A Priori Tests for the MIXMAX Random Number Generator

- Mathematics, Physics
- 2018

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 or… Expand

Spectral test of the MIXMAX random number generators

- Physics, Mathematics
- 2019

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-random… Expand

Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers

- Mathematics
- 2018

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 their… Expand

Review of High-Quality Random Number Generators

- Computer Science, Physics
- 2019

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

- Mathematics, Physics
- 2016

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 exponential… Expand

Anosov C-systems and random number generators

- Physics, Mathematics
- 2016

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

- Computer Science
- J. Inf. Secur. Appl.
- 2020

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

- Mathematics
- 2017

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. All… Expand

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