Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Entropy of pseudo-random-number generators.

Stephan Mertens1, Heiko Bauke

  • 1Institut für Theoretische Physik, Otto-von-Guericke Universität, PF 4120, 39016 Magdeburg, Germany. stephan.mertens@physik.uni-magdeburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
Summary

Pseudo-random number generators can fail in cluster Monte Carlo simulations due to low conditional entropy in their production rules. This fundamental mechanism, independent of sequence length, explains generator failures beyond empirical test limitations.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Percolation Is Odd.

Physical review letters·2019
Same author

SANRA-a scale for the quality assessment of narrative review articles.

Research integrity and peer review·2019
Same author

Percolation thresholds and Fisher exponents in hypercubic lattices.

Physical review. E·2018
Same author

Percolation thresholds in hyperbolic lattices.

Physical review. E·2018
Same author

Universal features of cluster numbers in percolation.

Physical review. E·2018
Same author

Percolation in finite matching lattices.

Physical review. E·2017

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Numerical Methods

Background:

  • Pseudo-random number generators (PRNGs) are crucial for simulations.
  • Previous work (Phys. Rev. Lett. 69, 3382 (1992)) highlighted PRNG failures in cluster Monte Carlo simulations.
  • The underlying cause of these failures has remained a key research question.

Purpose of the Study:

  • To elucidate the fundamental mechanism causing PRNG failures in cluster Monte Carlo simulations.
  • To identify a more profound quality measure for PRNGs beyond traditional empirical tests.

Main Methods:

  • Analysis of the mathematical structure of PRNGs, specifically their recurrence relations: x(i) = f(x(i-1), ..., x(i-q)).
  • Investigation of the conditional entropy of the production rule f() given the statistics of preceding values.

Related Experiment Videos

  • Comparison of conditional entropy as a quality measure against standard empirical testing methods.

    • Main Results:

    • PRNG failure in cluster Monte Carlo simulations is attributed to low conditional entropy of the production rule.
    • This low entropy arises from the dependence of the production rule on the statistics of previous numbers.
    • Conditional entropy is shown to be independent of the generator's lag (q) or period.

    Conclusions:

    • Conditional entropy provides a fundamental measure of PRNG quality for simulations.
    • This measure is more insightful than empirical tests, which have limited horizons.
    • Understanding conditional entropy is key to developing reliable PRNGs for advanced simulations.