Advertisement

Journal of Statistical Physics

, Volume 63, Issue 5–6, pp 883–896 | Cite as

The hierarchy of correlations in random binary sequences

  • Aaldert Compagner
Articles

Abstract

The meaning of randomness is studied for the simple case of binary sequences. Ensemble theory is used, together with correlation coefficients of any order. Conservation laws for the total amount of correlation are obtained. They imply that true randomness is an ensemble property and can never be achieved in a single sequence. The relation with entropy is discussed for different ensembles. Well-tempered pseudorandom sequences turn out to be suitable sources of random numbers, and practical recipes to generate them for use in large-scale Monte Carlo simulations are found.

Key words

Randomness correlation coefficients entropy random-number generation Monte Carlo calculations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. E. Knuth,The Art of Computer Programming, Vol. 2 (Addison-Wesley, 1981).Google Scholar
  2. 2.
    L. Afflerbach,J. Comp. Appl. Math. 31:3 (1990).Google Scholar
  3. 3.
    G. Marsaglia and A. Zaman, preprint (1990).Google Scholar
  4. 4.
    F. James,Comp. Phys. Commun. 60:329 (1990).Google Scholar
  5. 5.
    B. D. Ripley,J. Comp. Appl. Math. 31:153 (1990).Google Scholar
  6. 6.
    H. Niederreiter,Ann. Oper. Res., to be published.Google Scholar
  7. 7.
    M. van Lambalgen,J. Symbolic Logic 52:725 (1987); Ph. D. Thesis, University of Amsterdam (1987).Google Scholar
  8. 8.
    A. Compagner and A. Hoogland,J. Comp. Phys. 71:391 (1987).Google Scholar
  9. 9.
    A. Compagner,Am. J. Phys., to be published (1991).Google Scholar
  10. 10.
    S. W. Golomb,Shift Register Sequences (Holden-Day, 1967).Google Scholar
  11. 11.
    N. Zierler,Inform. Control 15:67 (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Aaldert Compagner
    • 1
  1. 1.Laboratory of Applied PhysicsDelftThe Netherlands

Personalised recommendations