How to improve a random number generator

Abstract

It is demonstrated that the one-dimensional random walk is sensitive both to short and long correlation of random numbers. In the case of correlated random numbers, the walker is trapped in the vicinity of the correlation. The result is a multipeak range distribution of the walker. Hence, the one-dimensional random walk can be used as a supplement to the standard tests for revealing long correlations of the generated random numbers. By implementing variety of tests to several generators we have shown that the quality can be improved by using a double randomization technique only if the random numbers, to be sampled from, are of a good quality. The sampling generator is less important. We propose, as well, a generator that produces high-quality random numbers for many stochastic processes.