On the assessment of random and quasi-random point sets. (English) Zbl 0937.65004

Hellekalek, Peter

Hellekalek, Peter (ed.) et al., Random and quasi-random point sets. New York, NY: Springer. Lect. Notes Stat. 138, 49-108 (1998).

This is a very useful survey article on the analysis of uniform pseudorandom numbers and low-discrepancy point sets. One aim of the author is to arrive at a unified viewpoint on the assessment of uniform pseudorandom numbers and low-discrepancy point sets. Central concepts for the author’s vantage point are the spectral test, the discrepancy, and the diaphony.
The paper provides rewarding reading both for the theoretician and the practitioner. The author shares a lot of his insights and offers poignant comments on the use of pseudorandom numbers and low-discrepancy point sets. One of the highlights of the paper is Section 5, in which a general version of the spectral test is introduced and analyzed.
For the entire collection see [Zbl 0903.00053].

Reviewer: H.Niederreiter (Wien)

MSC:

65C10	Random number generation in numerical analysis
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis
11-02	Research exposition (monographs, survey articles) pertaining to number theory
11K45	Pseudo-random numbers; Monte Carlo methods

Keywords:

survey; uniform pseudorandom numbers; low-discrepancy point sets; spectral test; discrepancy; diaphony

Software:

MersenneTwister; TESTPACK