Characterization of Brownian Gibbsian line ensembles

Evgeni Dimitrov, Konstantin Matetski

Published 2020-02-03Version 1

In this paper we show that a Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its top curve, i.e. the finite-dimensional sets of the its top curve form a separating class. A particular consequence of our result is that the Airy line ensemble is the unique Brownian Gibbsian line ensemble, whose top curve is the Airy$_2$ process.