Exactly solving the KPZ equation

Abstract

We present a complete proof of the exact formula for the one-point distribution for the narrow-wedge Hopf-Cole solution to the Kardar-Parisi-Zhang (KPZ) equation. This presentation is intended to be self-contained so no previous knowledge about stochastic PDEs, or exactly solvable systems is presumed.

This is a chapter in a forthcoming AMS Proceedings collection of expanded notes from the AMS Short Course "Random Growth Models," which took place in Atlanta, GA, at the AMS Joint Mathematics Meetings in January 2017. Editors: Michael Damron, Firas Rassoul-Agha, Timo Seppalainen