Parallelization of random number generators and long-range correlations

SummaryPartitions of pseudo-random sequences generated by congruential schemes are investigated for use on computer systems where multiple processing units run in parallel for the solution of a Monte Carlo problem. A special partition is suggested which ensures independence between the units working simultaneously, and yields reproducible sequences. The analysis performed has brought out the existence of strong autocorrelations between terms located far apart in the sequences, dependent only on the congruential nature of the generators. The study of these correlations — carried out in a number theoretic framework — points out that only small fractions of the sequences can be safely used.

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