LA Probability Forum

UCLA MSR 6627

We consider the KPZ equation on a half line with Neumann boundary condition. This model has seen significant recent attention due to the presence of a "depinning" phase transition and a rich phase diagram for its limiting distributions as the boundary strength varies. While scaling limits for the full-space KPZ equation have been studied extensively, much less is known in the half-space setting. In this talk, I will discuss results on the process-level long-time scaling limit of the half-space KPZ equation under 1:2:3 KPZ scaling. The key to the analysis is the construction of the novel half-space KPZ line ensemble, which satisfies a Brownian Gibbs property with pairwise attraction between curves at the boundary. We show more generally that this entire line ensemble is tight under KPZ scaling, and we describe its limit points as Brownian ensembles with pairwise pinning at the boundary. This is a joint work with Sayan Das.