Abstract
In this paper we show that a Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its top curve, that is, the finite-dimensional sets of the top curve form a separating class. A particular consequence of our result is that the parabolic Airy line ensemble is the unique Brownian Gibbsian line ensemble, whose top curve is the parabolic Airy2 process.
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