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Development and Implementation of new generation of Pseudo Random Number Generators based on Kolmogorov-Anosov K-systems

Deliverables

Critical Indices and Loop Integrals

The critical indices of random space-time manifolds, their Hausdorff dimensionality. The values of the scalar integrals representing quantum correction in decay branching ratios.

Statistical Data

"The statistical data : comulative distribution functions; Kolmogorov-Smirnov test;""BigCrush"" suite of tests; Shapiro-Wilk test; Anderson-Darling test representing internal characteristics of the MIXMAX generator as a function of the dimensionality N=256,508,1260 of the generator and of the order of the Galois field p=2^61 -1."

Multi-thread Programmes

An object-oriented software package designed and written in C++ ready to be used in ROOT and Geant4, together with on-line manual and validation tests to ensure its correctness.

MIXMAX generator

Program of the MIXMAX generator with tuneable internal parameters of maximal dimensionality N=256,509,1260 and of the order of the Galois field p=2^61-1, embedded into a user friendly environment and with an on-line manual.

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Publications

Бильярд Артина: экспоненциальный распад корреляционных функций

Author(s): Хасмик Рубеновна Погосян, Hasmik Rubenovna Poghosyan, Г М Бабуджян, H M Babujian, Георгий Константинович Саввиди, Georgii Konstantinovich Savvidi
Published in: Теоретическая и математическая физика, Issue 197/2, 2018, Page(s) 230-251, ISSN 0564-6162
DOI: 10.4213/tmf9549

Distribution of periodic trajectories of C-K systems MIXMAX pseudorandom number generator

Author(s): Andrzej Görlich, Marios Kalomenopoulos, Konstantin Savvidy, George Savvidy
Published in: International Journal of Modern Physics C, Issue Vol. 28, No. 2 (2017) 1750032 (16 pages), 2016, Page(s) 1750032, ISSN 0129-1831
DOI: 10.1142/S0129183117500322

Anosov C-systems and random number generators

Author(s): G. K. Savvidy
Published in: Theoretical and Mathematical Physics, Issue 188/2, 2016, Page(s) 1155-1171, ISSN 0040-5779
DOI: 10.1134/S004057791608002X

Classical Limit Theorems and High Entropy MIXMAX random number generator

Author(s): Hayk Poghosyan, Konstantin Savvidy and George Savvidy
Published in: Chaotic Modeling and Simulation, Issue 1 (2018) 79–89, 2018, Page(s) 79-89, ISSN 2241-0503

Spectral test of the MIXMAX random number generators


Published in: ISSN 0960-0779
DOI: 10.1016/j.chaos.2018.11.024

Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers


Published in: ISSN 0960-0779
DOI: 10.1016/j.chaos.2018.01.007

The MIXMAX random number generator

Author(s): Konstantin G. Savvidy,
Published in: Computer Physics Communications, Issue Volume 196, November 2015,, 2015, Page(s) Pages 161–165, ISSN 0010-4655
DOI: 10.1016/j.cpc.2015.06.003

Statistical Tests for MIXMAX Pseudorandom Number Generator

Author(s): Narek Martirosyan, Gevorg Karyan and Norayr Akopov
Published in: Mathematical Problems of Computer Science, Issue 47 (2017) 37-49, 2017, Page(s) 12 pages, ISSN 0131-4645

Spectrum and Entropy of C-systems. MIXMAX random number generator

Author(s): Konstantin Savvidy and George Savvidy
Published in: Chaos Solitons and Fractals: the interdisciplinary journal of Nonlinear Science,, Issue 91 (2016) 33-38, 2016, ISSN 0960-0779
DOI: 10.1016/j.chaos.2016.05.003

Correlation Functions of Classical and Quantum Artin System defined on Labachevsky Plane and Scrambling Time

Author(s): Brachia Babujian, Rubik Poghossian and George Savvidy
Published in: https://arxiv.org/abs/1808.02132, 2018

Quantum-Mechanical interpretation of Riemann zeta function zeros

Author(s): Konstantin Savvidy and George Savvidy
Published in: https://arxiv.org/abs/1809.09491, 2018

Classical limit theorems and high entropy MIXMAX random number generator

Author(s): Hayk Poghosyan, Konstantin Savvidy and George Savvidy
Published in: Proceedings of the 10th Chaotic Modeling and Simulation International Conference, Issue Barcelona, Spain: 30 May-2 June, 2017, 2017, Page(s) pages: 661-675