Recent trends in random number and random vector generation
Annals of Operations Research
On the statistical independence of nonlinear congruential pseudorandom numbers
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On a new class of pseudorandom numbers for simulation methods
Journal of Computational and Applied Mathematics
Average equidistribution properties of compound nonlinear congruential pseudorandom numbers
Mathematics of Computation
Average Behaviour of Compound Nonlinear Congruential Pseudorandom Numbers
Finite Fields and Their Applications
Linear and inversive pseudorandom numbers for parallel and distributed simulation
PADS '98 Proceedings of the twelfth workshop on Parallel and distributed simulation
On the statistical independence of compound pseudorandom numbers over part of the period
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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This paper deals with the general nonlinear congruential method for generating uniform pseudorandom numbers, in which permutation polynomials over finite prime fields play an important role. It is known that these pseudorandom numbers exhibit an attractive equidistribution and statistical independence behavior. In the context of parallelized simulation methods, a large number of parallel streams of pseudorandom numbers with strong mutual statistical independence properties are required. In the present paper, such properties of parallelized nonlinear congruential generators are studied based on the discrepancy of certain point sets. Upper and lower bounds for the discrepancy both over the full period and over (sufficiently large) parts of the period are established. The method of proof rests on the classical Weil bound for exponential sums.