Title: Large deviations of the KPZ equation

 

Abstract: The variational principle, or the least action principle, provides a framework for studying the large deviations of stochastic systems.The KPZ equation is a stochastic PDE that plays a central role in a class of random growth phenomena. In this talk, we will explore the large deviations for the KPZ equation through the lens of the variational principle. We will explain how to extract various limits of the most probable shape of the KPZ equation from the variational formula. Our method combines the ideas from probability, PDE and integrable systems.