Kardar-Parisi-Zhang universality class and the anchored Toom interface

Abstract

We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom [Commun. Math. Phys. 177, 727 (1996)CMPHAY0010-361610.1007/BF02099545].