Probability Seminar: High moments of the SHE and spacetime limit shapes of the KPZ equation

Consider the n-point, fixed-time large deviations of the Kardar–Parisi–Zhang (KPZ) equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a range of scaling regimes that allows time to be short, unit-order, and long. I will present a result (joint with Yier Lin) on the n-point Large Deviation Principle (LDP) and the corresponding spacetime limit shape. The proof is based on another work (of myself) on the multipoint moments of the Stochastic Heat Equation (SHE). I will explain how to analyze the moments via a system of attractive Brownian particles and how to use the moments to obtain the LDP and spacetime limit shape.