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

We report some results of computer simulations for two models of random walks in random environment (rwre) on the one-dimensional lattice Z^2 for fixed space–time configuration of the environment: a model with Markov dependence in time, and a “quasi stationary” model with long range space–time correlations. We compare with the corresponding results for a model with i.i.d. (in space time) environment. In the range of times available 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.