Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late times

TL;DR

This paper investigates large deviations of the height in 1D KPZ growth models at late times, providing exact rate functions and revealing a third order phase transition between strong and weak coupling phases.

Contribution

It offers the first exact rate functions for large deviations in both discrete and continuum KPZ models, and proposes a phase transition at late times.

Findings

Exact rate functions for discrete and continuum KPZ models.

Identification of a third order phase transition.

Evidence of a phase change from strong to weak coupling.

Abstract

We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the rate functions for the discrete single step growth model, as well as for the continuum KPZ equation in a droplet geometry. Based on our exact calculation of the rate functions we argue that models in the KPZ class undergo a third order phase transition from a strong coupling to a weak coupling phase, at late times.