# Spectral Analysis of the MIXMAX Random Number Generators

@article{LEcuyer2020SpectralAO, title={Spectral Analysis of the MIXMAX Random Number Generators}, author={Pierre L’Ecuyer and Paul Wambergue and Erwan Bourceret}, journal={INFORMS J. Comput.}, year={2020}, volume={32}, pages={135-144} }

We study the lattice structure of random number generators of the MIXMAX family, a class of matrix linear congruential generators that produce a vector of random numbers at each step. These generators were initially proposed and justified as close approximations to certain ergodic dynamical systems having the Kolmogorov K-mixing property, which implies a chaotic (fast-mixing) behavior. But for a K-mixing system, the matrix must have irrational entries, whereas for the MIXMAX it has only integer…

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