Abstract
The authors construct a simple model of ballistic motion in a random environment in an arbitrary number of dimensions. The motion is determined by a quenched set of random orthogonal matrices on a hypercubic lattice, relating incoming and outgoing directions at a particular site. They select, study and classify a set of these matrices which agree with intuitive notions of 'isotropy'. A mean field theory is constructed of the transition between localised and extended trajectories and a qualitative discussion of various features of the phase diagram is made.
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