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This article is cited in 9 scientific papers (total in 9 papers)
Anosov C-systems and random number generators
G. K. Savvidi Institute of Nuclear Physics, National Research Center "Demokritos", Athens, Greece
Abstract:
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. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.
Keywords:
Anosov C-system, hyperbolic dynamical system, Kolmogorov entropy, Monte Carlo method, high energy physics, elementary particle, lattice quantum chromodynamics.
Received: 22.07.2015
Citation:
G. K. Savvidi, “Anosov C-systems and random number generators”, TMF, 188:2 (2016), 223–243; Theoret. and Math. Phys., 188:2 (2016), 1155–1171
Linking options:
https://www.mathnet.ru/eng/tmf9012https://doi.org/10.4213/tmf9012 https://www.mathnet.ru/eng/tmf/v188/i2/p223
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Abstract page: | 347 | Full-text PDF : | 130 | References: | 58 | First page: | 14 |
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