Deterministic walks in random environments

Deterministic walks in random environments (DWRE) occupy an intermediate position between purely random (generated by random trials) and purely deterministic (generated by deterministic dynamical systems, e.g., by maps) models of diffusion. These models combine deterministic and probabilistic features. We review general properties of DWRE and demonstrate that, to a large extent, their dynamics and their statistics can be analyzed consecutively and separately. We also show that orbits of one-dimensional walks in rigid environments with non-constant rigidity almost surely visit each site infinitely many times.