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arXiv · 2103.01186

Characterization of $H$-Brownian Gibbsian line ensembles

Evgeni Dimitrov
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Abstract

In this paper we show that an $H$-Brownian Gibbsian line ensemble is completely characterized by the finite-dimensional marginals of its lowest indexed curve for a large class of interaction Hamiltonians $H$. A particular consequence of our result is that the KPZ line ensemble is the unique line ensemble that satisfies the $H_1$-Brownian Gibbs property with $H_1(x) = e^x$ and whose lowest indexed curve is equal to the Hopf-Cole solution to the narrow wedge KPZ equation.

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Evgeni Dimitrov. 2021-03-01. Characterization of $H$-Brownian Gibbsian line ensembles. https://doi.org/10.2140/pmp.2022.3.627

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