GEOMETRIC RANDOM INNER PRODUCT TEST AND RANDOMNESS OF π

Fatin Sezgin ()
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Fatin Sezgin: Department of Business Information Management, Bilkent University, Ankara 06800, Turkey

International Journal of Modern Physics C (IJMPC), 2009, vol. 20, issue 02, 295-311

Abstract: The Geometric Random Inner Product (GRIP) is a recently developed test method for randomness. As a relatively new method, its properties, weaknesses, and strengths are not well documented. In this paper, we provide a rigorous discussion of what the GRIP test measures, and point out specific classes of defects that it is able to diagnose. Our findings show that the GRIP test successfully detects series that have regularities in their first- or second-order differences, such as the Weyl and nested Weyl sequences. We compare and contrast the GRIP test to some of the existing conventional methods and show that it is particularly successful in diagnosing deficient random number generators with bad lattice structures and short periods. We also present an application of the GRIP test to the decimal digits of π.

Keywords: Geometric random inner products; random number generator; randomness testing; randomness of π; Monte Carlo; pseudorandom; 02.50.Cw; 02.50.Ng; 02.70Uu; 05.10.Ln (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0129183109013625

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