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We consider the Dyson Ferrari-Spohn diffusion $\mathcal{X}^N =(\mathcal{X}^N_1,\dots,\mathcal{X}^N_N)$, consisting of $N$ non-intersectingFerrari-Spohn diffusions $\mathcal{X}^N_1 > \cdots > \mathcal{X}^N_N > 0$ on$\mathbb{R}$. This object was introduced by Ioffe, Velenik, and Wachtel (2018)as a scaling limit for line ensembles of $N$ non-intersecting random walksabove a hard wall with area tilts, which model certain three-dimensionalinterfaces in statistical physics. It was shown by Ferrari and Shlosman (2023)that as $N\to\infty$, after a spatial shift of order $N^{2/3}$ and constantrescaling in time, the top curve $\mathcal{X}^N_1$ converges to the$\mathrm{Airy}_2$ process in the sense of finite-dimensional distributions. Weextend this result by showing that the full ensemble $\mathcal{X}^N$ convergeswith the same shift and time scaling to the Airy line ensemble in the topologyof uniform convergence on compact sets. In our argument we formulate a BrownianGibbs property with area tilts for $\mathcal{X}^N$, which we show is equivalentafter a global parabolic shift to the usual Brownian Gibbs property introducedby Corwin and Hammond (2014).

Uniform convergence of Dyson Ferrari-Spohn diffusions to the Airy line ensemble