THE RANLUX GENERATOR - RESONANCES IN A RANDOM-WALK TEST

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by L uscher and implemented by James. We confirm the good quality of this g enerator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk t est. We also find that the lagged Fibonacci and Subtract-with-Carry re cipes exhibit similar failures in the random walk test. A revised anal ysis of the corresponding dynamical systems leads to the observation o f resonances in the eigenvalues of Jacobi matrix.