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Are there hyperbolas in the scatter plots of inversive congruential pseudorandom numbers? (English) Zbl 0935.65002
Summary: Given a scatter plot of overlapping pairs \((x_n,x_{n+ 1})\) of pseudorandom numbers and the information that it stems from either a linear congruential or an inversive congruential generator with small modulus, it is usually no problem to guess the type of the generator: the points of a linear generator form a grid or lattice whereas inversive and explicit inversive congruential pseudorandom numbers exhibit hyperbola-like structures. We give an analytical description of this most eye-catching structural element of inversive congruential generators.

MSC:
65C10 Random number generation in numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods
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