41 research outputs found
Review of High-Quality Random Number Generators
This is a review of pseudorandom number generators (RNG's) of the highest
quality, suitable for use in the most demanding Monte Carlo calculations. All
the RNG's we recommend here are based on the Kolmogorov-Anosov theory of mixing
in classical mechanical systems, which guarantees under certain conditions and
in certain asymptotic limits, that points on the trajectories of these systems
can be used to produce random number sequences of exceptional quality. We
outline this theory of mixing and establish criteria for deciding which RNG's
are sufficiently good approximations to the ideal mathematical systems that
guarantee highest quality. The well-known RANLUX (at highest luxury level) and
its recent variant RANLUX++ are seen to meet our criteria, and some of the
proposed versions of MIXMAX can be modified easily to meet the same criteria.Comment: 21 pages, 4 figure
Distribution of periodic trajectories of Anosov C-system
The hyperbolic Anosov C-systems have a countable set of everywhere dense
periodic trajectories which have been recently used to generate pseudorandom
numbers. The asymptotic distribution of periodic trajectories of C-systems with
periods less than a given number is well known, but a deviation of this
distribution from its asymptotic behaviour is less known. Using fast
algorithms, we are studying the exact distribution of periodic trajectories and
their deviation from asymptotic behaviour for hyperbolic C-systems which are
defined on high dimensional tori and are used for Monte-Carlo simulations. A
particular C-system which we consider in this article is the one which was
implemented in the MIXMAX generator of pseudorandom numbers. The generator has
the best combination of speed, reasonable size of the state, and availability
for implementing the parallelization and is currently available generator in
the ROOT and CLHEP software packages at CERN.Comment: 22 pages, 14 figure