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September 2021 Characterization of Brownian Gibbsian line ensembles
Evgeni Dimitrov, Konstantin Matetski
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Ann. Probab. 49(5): 2477-2529 (September 2021). DOI: 10.1214/21-AOP1513

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

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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

Information

Received: 1 March 2020; Revised: 1 January 2021; Published: September 2021
First available in Project Euclid: 24 September 2021

Digital Object Identifier: 10.1214/21-AOP1513

Subjects:
Primary: 82C22
Secondary: 60J65

Keywords: Airy line ensemble , Airy process , Gibbs measures

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 5 • September 2021
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