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Entropy of pseudo-random-number generators

Stephan Mertens and Heiko Bauke
Phys. Rev. E 69, 055702(R) – Published 21 May 2004

Abstract

Since the work of Ferrenberg et al. [Phys. Rev. Lett. 69, 3382 (1992)] some pseudo-random-number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed. Almost all random-number generators calculate a new pseudo-random-number xi from preceding values, xi=f(xi1,xi2,,xiq). Failure of these generators in cluster Monte Carlo simulations and related experiments can be attributed to the low entropy of the production rule f() conditioned on the statistics of the input values xi1,,xiq. Being a measure only of the arithmetic operations in the generator rule, the conditional entropy is independent of the lag in the recurrence or the period of the sequence. In that sense it measures a more profound quality of a random-number generator than empirical tests with their limited horizon.

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  • Received 19 November 2003

DOI:https://doi.org/10.1103/PhysRevE.69.055702

©2004 American Physical Society

Authors & Affiliations

Stephan Mertens* and Heiko Bauke

  • Institut für Theoretische Physik, Otto-von-Guericke Universität, PF 4120, 39016 Magdeburg, Germany

  • *Email address: stephan.mertens@physik.uni-magdeburg.de
  • Email address: heiko.bauke@physik.uni-magdeburg.de

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Issue

Vol. 69, Iss. 5 — May 2004

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