Characterization of $H$-Brownian Gibbsian line ensembles

Abstract

In this paper 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 Hopf-Cole solution to the narrow wedge KPZ equation.

47 pages, 6 figures. Fixed some typos in the previous version of the paper. arXiv admin note: text overlap with arXiv:2002.00684

References in corpus (3)

• The one-dimensional KPZ equation and its universality class
• Bulk properties of the Airy line ensemble
• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles