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

TL;DR

This paper investigates how quenched noise affects the growth patterns of a deterministic cellular automaton, revealing a transition from recurrence to transience and Tracy-Widom fluctuations in the boundary growth, classified within a specific percolation universality class.

Contribution

It introduces the first analysis of a recurrence-transience transition in a cellular automaton with quenched noise, linking it to the 3D Anisotropic Directed Percolation universality class.

Findings

Boundary fluctuations follow Tracy-Widom distribution.

Transition from recurrent to transient walk with increasing noise.

Transition belongs to the 3D Anisotropic Directed Percolation universality class.

Abstract

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.