Alexander Dunlap
Duke University
Room: M3 3127
Stationary measure for the open KPZ equation: an analytic viewpoint
The KPZ equation is a popular model for the growth of a random interface. The "open" variant of this equation describes the growth of the interface when a reflection symmetry corresponding to Neumann boundary conditions is imposed.
I will describe an analytic approach to proving the invariance of the stationary measure for the inhomogeneous open KPZ equation, given the knowledge of the (Brownian) stationary measure for the problem with homogeneous boundary conditions. In place of tools from integrable probability, we use a time-reversal argument and Itô’s formula to reduce the problem to a statement about the behavior of the KPZ nonlinearity at the boundary. We then use the theory of regularity structures to prove this statement. Joint work with Yu Gu and Tommaso Rosati.