KPZ equation in one dimension and line ensembles

TL;DR

This paper discusses the KPZ equation in one dimension, focusing on discretized models and the use of line ensembles with entropic repulsion to derive exact scaling functions like the stationary two-point function.

Contribution

It explains the method of line ensembles with entropic repulsion, a key technique for obtaining exact results in discretized KPZ models.

Findings

Exact scaling functions for discretized KPZ models

Derivation of stationary two-point function

Explanation of line ensemble methodology

Abstract

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.