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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Ronald C. Blakey,Wayne D. Ranneythe “..” This chapter deals with the general case, that is, given an n dimensional random vector X and a collection of n by n matrices, .(.); . ∈ . ⊂ IR, attention is focused on conditions under which (.(.).)(mod 1) converges to a distribution uniform on the unit hypercube, ., as . tends to infinity.

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Bivalvia in Ancient Hydrocarbon SeepsThere are many ways of introducing the concept of probability in classical, i.e. deterministic physics. This work is concerned with one approach, known as “the method of arbitrary functions.” To illustrate it consider the following example:

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https://doi.org/10.1007/978-0-8176-4695-0r of (.)(mod 1) = ((.). (mod 1),..., (.)(mod 1)) is studied in detail in Sect.4.1. A necessary and sufficient condition for weak-star convergence of (.)(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

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https://doi.org/10.1007/978-1-4419-8684-9Generator; Mathematica; Rang; Variation; dynamical systems; ergodic theory; modeling; probability