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Spectrum and entropy of C-systems MIXMAX random number generator
- Source :
- Chaos Solitons and Fractals: the interdisciplinary journal of Nonlinear Science
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 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 instability of all their trajectories and as such have mixing of all orders, nonzero Kolmogorov entropy and a countable set of everywhere dense periodic trajectories. In this paper we are studying the properties of their spectrum and of the entropy. For a two-parameter family of C-system operators A(N,s), parametrised by the integers N and s, we found the universal limiting form of the spectrum, the dependence of entropy on N and the period of its trajectories on a rational sublattice. One can deduce from this result that the entropy and the periods are sharply increasing with N. We present a new three-parameter family of C-operators A(N,s,m) and analyse the dependence of its spectrum and of the entropy on the parameter m. We developed our earlier suggestion to use these tuneable Anosov C-systems for multipurpos Monte-Carlo simulations. The MIXMAX family of random number generators based on Anosov C-systems provide high quality statistical properties, thanks to their large entropy, have the best combination of speed, reasonable size of the state, tuneable parameters and availability for implementing the parallelisation.<br />12 pages, 5 figures, references, comments and a note added
- Subjects :
- Random number generation
General Mathematics
Configuration entropy
FOS: Physical sciences
General Physics and Astronomy
Dynamical Systems (math.DS)
010103 numerical & computational mathematics
Maximum entropy spectral estimation
01 natural sciences
010305 fluids & plasmas
Binary entropy function
High Energy Physics - Phenomenology (hep-ph)
High Energy Physics - Lattice
0103 physical sciences
FOS: Mathematics
Countable set
Statistical physics
Mathematics - Dynamical Systems
0101 mathematics
Entropy rate
Mathematics
Applied Mathematics
High Energy Physics - Lattice (hep-lat)
Mathematical analysis
Statistical and Nonlinear Physics
High Energy Physics - Phenomenology
Maximum entropy probability distribution
Joint quantum entropy
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 91
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi.dedup.....91b19877878f4683b928d11457a9197d