Long-range correlations in linear and non-linear random number generators
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).
scientific article; zbMATH DE number 4172232