LONG-RANGE CORRELATIONS IN LINEAR AND NONLINEAR RANDOM NUMBER GENERATORS

Parallel use of pseudorandom numbers requires founded confidence on the mutual independence of the separate sequences. The authors (Numer. Math. 53 (1988) 595) have pointed out that sequences generated by linear congruential methods and equipartitioned among the concurrent processors, contain strong long-range correlations. It is shown here that this phenomenon is not restricted to linear schemes. It appears in any recursive periodic algorithm of the form xn ≡ f{hook}(xn-1)(mod 2t) if the generation rule is such that the period halves when the modulus halves. © 1990.