The KPZ equation is a fundamental stochastic PDE related to random growth processes, Burgers turbulence, interacting particle systems, directed polymers and random matrix theory. In this talk we probe the large deviation behaviors of the solution. Namely, we consider the probability that the solution is much smaller than expected. Our investigation is assisted by an exact identity relating the KPZ equation to the Airy point process (which arises at the edge of the spectrum for random Hermitian symmetric matrices). Time permitting, we will also discuss similar works-in-progress related the asymmetric simple exclusion process and stochastic six vertex model.

No prior knowledge about KPZ will be assumed in this talk. This work is joint with my graduate student Promit Ghosal.