Computer simulations for some one-dimensional models of random walks in fluctuating random environment

Summary: "We report some results of computer simulations for two models of random walks in random environment (rwre) on the one-dimensional lattice Z for fixed space-time configuration of the environment (`quenched rwre'): a `Markov model' with Markov dependence in time, and a `quasi-stationary' model with long range space-time correlations. We compare the corresponding results for a model with an i.i.d. (in space-time) environment. In the range of times available to us the quenched distributions of the random walk displacement are far from Gaussian, but as the behavior is similar for all three models one cannot exclude asymptotic Gaussianity, which is proved for the model with i.i.d. environment. We also report results on the random drift and on some time correlations which show a clear power decay.''