Efficiency test of pseudorandom number generators using random walks

Markov chain Monte Carlo methods and computer simulations usually use long sequences of random numbers generated by deterministic rules, so-called pseudorandom number generators. Their efficiency depends on the convergence rate to the stationary distribution and the quality of random numbers used for simulations. Various methods have been employed to measure the convergence rate to the stationary distribution, but the effect of random numbers has not been much discussed. We present how to test the efficiency of pseudorandom number generators using random walks.