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.
Funding Statement
Both authors are partially supported by the Minerva Foundation Fellowship.
Acknowledgments
We would like to thank Alexei Borodin, Ivan Corwin, Vadim Gorin and the anonymous referees for useful comments on earlier drafts of this paper. We also thank Julien Dubédat for suggesting some useful literature and Alisa Knizel for some of the figures.
Citation
Evgeni Dimitrov. Konstantin Matetski. "Characterization of Brownian Gibbsian line ensembles." Ann. Probab. 49 (5) 2477 - 2529, September 2021. https://doi.org/10.1214/21-AOP1513
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