Large deviations of the KPZ equation via the Stochastic Airy Operator

TL;DR

This paper reviews methods for establishing the lower-tail large deviation principle for the KPZ equation, focusing on the connection with the Stochastic Airy Operator, to understand rare fluctuation events.

Contribution

It synthesizes and discusses the approach of Tsai (2018) for proving large deviations in the KPZ equation using spectral analysis of the Stochastic Airy Operator.

Findings

Clarifies the link between KPZ large deviations and spectral properties of the Stochastic Airy Operator

Provides insights into the techniques for lower-tail large deviation proofs in stochastic PDEs

Summarizes key ideas from Tsai (2018) for future research directions

Abstract

In this article we review the ideas in Tsai (2018) toward proving the one-point, lower-tail large deviation principle for the Kardar--Parisi--Zhang equation.