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Titlebook: A Road to Randomness in Physical Systems; Eduardo M. R. A. Engel Book 1992 Springer-Verlag Berlin Heidelberg 1992 Generator.Mathematica.Ra

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Book 1992known as "the method of arbitrary funetionJ. " It was put forward by Poincare in 1896 and developed by Hopf in the 1930‘s. The idea is the following. There is always some uncertainty in our knowledge of both the initial conditions and the values of the physical constants that characterize the evolut
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https://doi.org/10.1007/978-0-8176-4695-0.)(mod 1) to a distribution uniform on [0, l]., ., as . tends to infinity, is established in Theorem 4.2 (Borel, Hopf, Kallenberg). The random vector (.)(mod 1) converges to . in the variation distance if and only if . has a density (Theorem 5.3).
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