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Characterization of
$H$-Brownian Gibbsian line ensembles
Evgeni Dimitrov |
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Vol. 3 (2022), No. 3, 627–673
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Abstract |
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We show that an -Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its lowest-indexed curve for a large class of interaction Hamiltonians . A particular consequence of our result is that the KPZ line ensemble is the unique line ensemble that satisfies the -Brownian Gibbs property with and whose lowest-indexed curve is equal to the Cole–Hopf solution to the narrow wedge KPZ equation. |
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Keywords
Gibbsian line ensemble, KPZ line ensemble
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Mathematical Subject Classification
Primary: 60J65
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Milestones
Received: 25 March 2021
Revised: 9 December 2021
Accepted: 22 December 2021
Published: 12 December 2022
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Authors |
| Evgeni Dimitrov | |
| Department of Mathematics Columbia University New York, NY United States |
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