Abstract
In a first step the definition of randomness and the mathematical definition of random numbers and sequences are addressed. We move on to describe the properties of an ideal random number generator and concentrate then on pseudo-random number generators which are the basic tool in the application of stochastic methods in Computational Physics. Statistical tests to check on the quality of random numbers are discussed in the last part of this chapter.
This is a preview of subscription content, log in via an institution.
Notes
- 1.
From now on we define quite generally the interval out of which random numbers x n are drawn by x n ∈ [0, 1] keeping in mind that this interval depends on the actual method applied. This method determines whether zero or one is contained in the interval.
References
Coffey, W.T., Kalmykov, Y.P.: The Langevin Equation, 3rd edn. World Scientific Series in Contemporary Chemical Physics: Volume 27. World Scientific, Hackensack (2012)
Dubitzky, W., Wolkenhauer, O., Cho, K.H., Yokota, H. (eds.): Encyclopedia of Systems Biology, p. 1596. Springer, Berlin/Heidelberg (2013)
Tapiero, C.S.: Risk and Financial Management: Mathematical and Computational Methods. Wiley, New York (2004)
Lax, M., Cai, W., Xu, M.: Random Processes in Physics and Finance. Oxford Finance Series. Oxford University Press, Oxford (2013)
Laing, C., Lord, G.J. (eds.): Stochastic Methods in Neuroscience. Oxford University Press, Oxford (2009)
Chaitin, G.J.: Randomness and mathematical proof. Sci. Am. 232, 47 (1975)
Knuth, D.: The Art of Computer Programming, vol. II, 3rd edn. Addison Wesley, Menlo Park (1998)
Gentle, J.E.: Random Number Generation and Monte Carlo Methods. Statistics and Computing. Springer, Berlin/Heidelberg (2003)
Ripley, B.D.: Stochastic Simulation. Wiley, New York (2006)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++, 2nd edn. Cambridge University Press, Cambridge (2002)
Knuth, D.: The Art of Computer Programming, vol. IV. Addison Wesley, Menlo Park (2011)
Marsaglia, G., Zaman, A.: A new class of random number generators. Ann. Appl. Prob. 1, 462–480 (1991)
Iversen, G.P., Gergen, I.: Statistics. Springer Undergraduate Textbooks in Statistics. Springer, Berlin/Heidelberg (1997)
Keener, R.W.: Theoretical Statistics. Springer, Berlin/Heidelberg (2010)
Chow, Y.S., Teicher, H.: Probability Theory, 3rd edn. Springer Texts in Statistics. Springer, Berlin/Heidelberg (1997)
Kienke, A.: Probability Theory. Universitext. Springer, Berlin/Heidelberg (2008)
Abramovitz, M., Stegun, I.A. (eds.): Handbook of Mathemathical Functions. Dover, New York (1965)
Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Stickler, B.A., Schachinger, E. (2016). Pseudo-random Number Generators. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-27265-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-27265-8_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27263-4
Online ISBN: 978-3-319-27265-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)