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Characterization of Brownian Gibbsian line ensembles (2002.00684v2)
Published 3 Feb 2020 in math.PR, math-ph, and math.MP
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.
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