A novel Recurrence-Transience transition and Tracy-Widom growth in a cellular automaton with quenched noise

23 Jul 2018 Dandekar Rahul

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... (read more)

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  • STATISTICAL MECHANICS
  • MATHEMATICAL PHYSICS
  • MATHEMATICAL PHYSICS