A novel recurrence-transience transition and Tracy-Widom growth in a cellular automaton with quenched noise

We study the growing patterns formed by a deterministic cellular automaton, the rotor-router model, in the presence of quenched noise. By the detailed study of two cases, we show that: a) the boundary of the pattern displays KPZ fluctuations with a Tracy-Widom distribution, b) as one increases the amount of randomness, the rotor-router path undergoes a transition from a recurrent to a transient walk. This transition is analysed here for the first time, and it is shown that it falls in the 3D anisotropic directed percolation universality class.