Finally, we wax philosophical. We urge the supercomputist to approach the generation of random numbers with circumspection, particularly when solving very large-scale problems. All random number generators should be tested thoroughly for their quality before being used upon other than academic problems. Further, at least two levels of quality in random number generators should be implemented to assess whether the answers are independent of the random numbers. This is a matter requiring judgment and is aided by experience.
However, the situation is not as bleak as it may seem from the above discussion. For very large scale problems lacking a regular structure (e.g., complex geometries and/or material properties), it is very unlikely that correlations between random numbers generated on separate processors will be significant due to the fact that the physical problem exhibits a great many possibilities for random events. Further, if the parameters of the generator are chosen correctly, there are a great many possibilities for random events when using random real numbers. However, the truly cautious researcher should not rely on the confluence of these factors to discourage assessing the results in the context of quality of the random events derived from the random number generator.
Further, it is wise to mention that the above observations are specific to using random real numbers, and not random integers. In particular, there may exist a resonance between the physical problem and random integers such as the successive odd/even pairs obtained when using a modulus of a power of two in a linear, congruential generator. As the complexity of the problem decreases, the potential for problems with the random number generator increases.