# The KPZ Universality Class and Related Topics

## TL;DR

This paper provides a comprehensive introduction to the KPZ universality class, exploring its properties, scaling behaviors, and connections to the asymmetric simple exclusion process, highlighting its integrability and exact formulas.

## Contribution

It offers a detailed analysis of the KPZ universality class through discrete approximations like ASEP, emphasizing its integrability and exact solvability.

## Key findings

- Characterization of KPZ scaling exponents
- Limiting statistics of KPZ class processes
- Exact formulas derived from ASEP integrability

## Abstract

These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions related to random growth processes in $1+1$ dimensions. We describe some of the characteristic properties of the KPZ universality class such as scaling exponents and limiting statistics. In particular, we aim to extract the characteristic properties of the KPZ universality class by understanding the KPZ stochastic partial differential equation by a special discrete approximation given by the asymmetric simple exclusion process (ASEP). The connection with the ASEP is very important as the process enjoys a rich integrability structure that leads to many exact formulas.