The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

TL;DR

This paper provides an exact solution to the 1+1 dimensional KPZ equation with sharp wedge initial conditions, confirming its universality class and detailed distribution properties in the long-term limit.

Contribution

It offers the first exact solution for the KPZ equation with specific initial conditions, validating its universality class and distribution characteristics.

Findings

Confirmed the KPZ universality class for the model

Derived the full probability distribution of height fluctuations

Validated scaling exponents and distribution in the long time limit

Abstract

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.