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Characterization of $H$-Brownian Gibbsian line ensembles

Evgeni Dimitrov

Vol. 3 (2022), No. 3, 627–673
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 H1-Brownian Gibbs property with H1(x) = ex and whose lowest-indexed curve is equal to the Cole–Hopf solution to the narrow wedge KPZ equation.

Keywords
Gibbsian line ensemble, KPZ line ensemble
Mathematical Subject Classification
Primary: 60J65
Milestones
Received: 25 March 2021
Revised: 9 December 2021
Accepted: 22 December 2021
Published: 12 December 2022
Authors
Evgeni Dimitrov
Department of Mathematics
Columbia University
New York, NY
United States