A brief introduction to KPZ equation and KPZ universality

Abstract

In this survey, we shall first introduce the physical background of KPZ universality class. The Eden model, sticky block model and KPZ equation will be mentioned. Then we shall focus on the Cole-Hopf solution to 1-dimensional KPZ equation and present some discrete models like the corner growth model and directed polymer model, which could converge to the KPZ equation in some sense.