An appetizer to modern developments on the Kardar-Parisi-Zhang universality class

TL;DR

This paper introduces the KPZ universality class, highlighting recent mathematical and experimental advances since 2000, and aims to make these developments accessible to non-specialists with a focus on physical insights.

Contribution

It provides an accessible overview of the KPZ class, emphasizing physical implications of mathematical progress and including experimental insights from liquid-crystal studies.

Findings

Recent mathematical solutions have deepened understanding of KPZ properties.

Experimental results support theoretical predictions of KPZ universality.

The review emphasizes physical intuition over complex mathematics.

Abstract

The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics -- as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.