The theory of the pseudorandom number generators takes a new shape thanks to the result and efforts of the MIXMAX Consortium in applying the cutting edge results of the Ergodic Theory to generate high quality random sequences for Monte-Carlo simulations [1,2,3,4]. A bases of the Consortium new approach is lying on the fundamental work of Anosov on hyperbolic C-systems [5] and on Kolmogorov theory of K-systems of nonzero entropy [6]. The two years of research and development by the Consortium resulted in the production of efficient C and C++ codes of the MIXMAX generator [1,3]. The C and C++ codes of the MIXMAX generator have been published in [1,3] and are publicly avalabel in the depository HEPFORGE.ORG [7] as well as on the webpage of the Consortium [8]. The webpage for the MIXMAX Consortium [8] reflects all aspects of the development of the project. For the needs of the Geant4 and CLHEP software packages at CERN the Consortium has developed the efficient low dimensional MIXMAX generators of dimension N = 8, 17, 40, 60, 96, 120 and 240. These generators have an advantage of having a very high quality sequence for moderate and small values of N. The Complex Statistical Tests of the MIXMAX pseudo random number generators were performed and demonstared that the MIXMAX is a unique 64-bit random number generator which is passing all BigCrushU01 tests [9], the PractRand tests, Dieharder test and many others. It was concluded that the two years (2015-2016) Milestone has been reached and assessment of the results in the execution of the Work packages have been presented at the MTR Meeting [10,11,12].
[1] K.Savvidy The MIXMAX random number generator, Comput.Phys.Commun. 196 (2015) 161-165.
(
http://dx.doi.org/10.1016/j.cpc.2015.06.003)(s’ouvre dans une nouvelle fenêtre); arXiv:1404.5355
[2] G. Savvidy, Anosov C-systems and random number generators, Theor.Math.Phys. 188 (2016) 1155-
1171; arXiv:1507.06348 [hep-th].
[3] K. Savvidy and G. Savvidy, Spectrum and Entropy of C-systems. MIXMAX random number generator,
Chaos Solitons Fractals 91 (2016) 33 ( doi:10.1016/j.chaos.2016.05.003); [arXiv:1510.06274
[math.DS]].
[4] A. Görlich, M. Kalomenopoulos, K. Savvidy and G. Savvidy, Distribution of periodic trajectories
of Anosov C-system, Int. J. Mod. Phys. C 28 (2017) 1750032 (doi: 10.1142/S0129183117500322)
[5] D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Trudy Mat.
Inst. Steklov., Vol. 90 (1967) 3 - 210
[6] A.N. Kolmogorov, New metrical invariant of transitive dynamical systems and automorphisms of
Lebesgue spaces, Dokl. Acad. Nauk SSSR, 119 (1958) 861-865
[7] HEPFORGE.ORG
http://mixmax.hepforge.org(s’ouvre dans une nouvelle fenêtre);
http://www.inp.demokritos.gr/˜savvidy/mixmax.php(s’ouvre dans une nouvelle fenêtre)[8]http://www.inp.demokritos.gr/˜savvidy/mixmax.php
[9] P. L’Ecuyer and R. Simard, TestU01: A C Library for Empirical Testing of Random Number
Generators, ACM Transactions on Mathematical Software, 33 (2007) 1-40.
[10] First Consortium Meeting and Workshop at CERN, July 2015:
https://indico.cern.ch/event/404547(s’ouvre dans une nouvelle fenêtre)[11] The Second Consortium Meeting and Workshop at CERN, July 2016:https://indico.cern.ch/event/544108/
[12]Conference and MTR Meeting in Athens, September 2016:https://indico.cern.ch/event/558996/