Characterization of Brownian Gibbsian line ensembles

Abstract

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.

48 pages, 7 figures; Fixed a few typos and added a new corollary