Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers

Abstract

We are developing further our earlier suggestion to use high entropy Anosov C-systems for the Monte-Carlo simulations. The hyperbolic Anosov C-systems have exponential instability of their trajectories and as such have mixing of all orders and nonzero Kolmogorov entropy. Of special interest are C-systems that are defined on a high dimensional torus. The C-systems on a torus are perfect candidates to be used for Monte-Carlo simulations. The correlation functions of the physical observables which are defined on a torus phase space are tend to zero and become uncorrelated exponentially fast. It is important to specify the parameters of a dynamical C-system which quantify the exponential decay. We have found that the upper bound on the rate of the exponential decay of the correlation functions universally depends on the value of the system entropy. This result allows to define decorrelation and relaxation times in terms of entropy and characterise the statistical properties of the MIXMAX generator.