×

Long-range correlations in linear and non-linear random number generators. (English) Zbl 0712.65005

This paper generalizes the authors’ earlier results [Numer. Math. 53, 595-608 (1988; Zbl 0633.65006)]. Consider the sequence \(\{x_ n\}\), \(n=1,2,3,..\). \(x_{n+1}=f(x_ n)mod m\). Let the generation rule fulfil the condition that the period halves when the module m halves. Let \(L=2d\) be the period of the generator. Then the points \((x_ n,x_{n+d})\) lie in no more than two parallel lines in the square with the side m. This result shows that it is necessary to discard half of the generated sequence for almost all known generators (e.g. inversive generators).
Reviewer: J.Král

MSC:

65C10 Random number generation in numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods

Citations:

Zbl 0633.65006
PDFBibTeX XMLCite
Full Text: DOI