KPZ universality class and the anchored Toom interface

TL;DR

This paper applies KPZ scaling theory to the anchored Toom interface, demonstrating that its fluctuations follow the Airy_1 process with no free parameters, confirmed by numerical evidence.

Contribution

It establishes a connection between the anchored Toom interface fluctuations and the KPZ universality class using Airy_1 process predictions.

Findings

Interface fluctuations follow the Airy_1 process

Spatial fluctuations match GOE Tracy-Widom distribution

Numerical results confirm theoretical predictions

Abstract

We revisit the anchored Toom interface and use KPZ scaling theory to argue that the interface fluctuations are governed by the Airy_1 process with the role of space and time interchanged. There is no free parameter. The predictions are numerically well confirmed for space-time statistics in the stationary state. In particular the spatial fluctuations of the interface are given by the GOE edge distribution of Tracy and Widom.