Characterization of $H$-Brownian Gibbsian line ensembles
Probability
2023-02-22 v2 Mathematical Physics
math.MP
Abstract
In this paper we show that an -Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its lowest indexed curve for a large class of interaction Hamiltonians . A particular consequence of our result is that the KPZ line ensemble is the unique line ensemble that satisfies the -Brownian Gibbs property with and whose lowest indexed curve is equal to the Hopf-Cole solution to the narrow wedge KPZ equation.
Keywords
Cite
@article{arxiv.2103.01186,
title = {Characterization of $H$-Brownian Gibbsian line ensembles},
author = {Evgeni Dimitrov},
journal= {arXiv preprint arXiv:2103.01186},
year = {2023}
}
Comments
47 pages, 6 figures. Fixed some typos in the previous version of the paper. arXiv admin note: text overlap with arXiv:2002.00684