Abstract

We show that an $H$-Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its lowest-indexed curve for a large class of interaction Hamiltonians $H$. A particular consequence of our result is that the KPZ line ensemble is the unique line ensemble that satisfies the $H_1$-Brownian Gibbs property with $H_1(x)=e^x$ and whose lowest-indexed curve is equal to the Cole–Hopf solution to the narrow wedge KPZ equation.

Keywords

Mathematical Subject Classification

Milestones

Authors