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from Part I - Finite Abelian Groups
Published online by Cambridge University Press: 06 July 2010
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.
J. von NeumannIn the first part of this chapter we obtain limit theorems for the simplest random walks on ℤ/nℤ, for n odd, using the DFT and Markov chains. In the second part we redo some of the first part, replacing Markov chains with sums of random variables. We begin with the example of random number generators.
References for this chapter include: Fan Chung [1996], F. Chung, P. Diaconis, and R. Graham [1987], P. Diaconis [1988], P. Diaconis and M. Shashahani [1986], P. Diaconis and D. Stroock [1987], P. Doyle and J. L. Snell [1984], W. Feller [1968], R. Guy [1984, Vol. 3, Section K45], J. G. Kemeny and J. L. Snell [1960], W. LeVeque [1974, Vol. 3, Section K45], K. Rosen [1993, Section 8.7], J. T. Sandefur [1990], J. L. Snell [1975], and M. Schroeder [1986, Chapter 27]. See also Chapters 17 and 18 for more information on random number generators.
Random Number Generators
There are many reasons why programs such as Mathematica and Matlab are capable of giving us a random number at the drop of a hat or the push of a key. Applications include computer simulations, sampling, testing of computer algorithms, decision making, Monte Carlo methods for numerical integration, and fault detection.
In the “good” old days, people obtained random numbers from tables.
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