Framework for testing random numbers in parallel calculations

We propose a framework for testing the quality of random numbers in parallel calculations. The key idea is to study cross-correlations between distinct sequences of random numbers via correlations between various diffusing random walkers, each of which is governed by a distinct random number sequence. The asymptotic power-law behavior of the corresponding correlation functions yields exponents, which can be compared with exact theoretical results. Correlations prior to the asymptotic regime can be further investigated by other complementary methods. We demonstrate this approach by three efficient tests, which find correlations in various commonly used pseudorandom number generators. Finally, we discuss some ideas for applying this framework in other contexts.