Abstract
A numerical study of deterministic motion in a random environment in two dimensions is performed. All trajectories are localised except at two isolated points in the parameter space. The distribution of trajectory lengths shows “critical” behaviour as those points are approached. Contact with an analytic estimate, based on analogy with gelation theory, is made in one region of the parameter space. The spatial extent of the trajectories scales with arc length as if they were ideal random walks, surprisingly.
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Salmeron, J., Ortuno, M. & Gunn, J.M.F. Critical behaviour in deterministic motion in a random environment. Z. Physik B - Condensed Matter 70, 269–274 (1988). https://doi.org/10.1007/BF01318308
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DOI: https://doi.org/10.1007/BF01318308