Percolation and motion in a simple random environment

The authors present a particularly simple model of deterministic classical motion in a two-dimensional random environment. As the parameters of the model are varied, a transition occurs from all trajectories being localised to some being extended. They construct a mean-field theory for this transition, and relate the model exactly to percolation models in particular parameter ranges. They point out that it is a member of a new class of site percolation analogues of direct bond percolation.