Time correlation and tail probabilities of the KPZ equation
Abstract: The KPZ equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle system, random polymers etc. In this talk, we focus on the time correlation and the tail probabilities of the solution of the KPZ equation. We investigate the correlation function of the KPZ equation at two different times. This will be based on a recent joint work with Prof. Alan Hammond from UC Berkeley and my advisor Prof. Ivan Corwin. One of the key inputs to the time correlation project is an estimate on the tail probabilities of the KPZ equation which we also describe. The discussion on the tail probabilities will be based on a separate joint work with Prof. Ivan Corwin. Our analysis is based on an exact identity between the KPZ equation and the Airy point process (which arises at the edge of the spectrum of the random Hermitian matrices) and the Brownian Gibbs property of the KPZ line ensemble.