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Entropy of pseudo-random-number generators.

Authors
  • Mertens, Stephan
  • Bauke, Heiko
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
May 01, 2004
Volume
69
Issue
5 Pt 2
Pages
55702–55702
Identifiers
PMID: 15244876
Source
Medline
License
Unknown

Abstract

Since the work of 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 x(i) from preceding values, x(i) =f( x(i-1), x(i-2), ..., x(i-q) ). 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 x(i-1), ..., x(i-q). 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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