Two applications for estimating Pi using MIXMAX random number generator and Monte Carlo method

We review some pseudo-random number generators (PRNGs) based on the theory of mixing in classical mechanical systems. In particular, we explore in detail the statistical characteristics of MIXMAX pseudo-random number generator such as its entropy, period and spectrum. We then apply this generator along with Monte Carlo method to estimate the value of Pi in two different ways, using the relation between approximated areas. We compare these results with those obtained using MATLAB’s default PRNG. The results of these simulations show the effectiveness, precision, consistency and viability of the random numbers generated by MIXMAX.