The Airy${}_2$ process and the 3D Ising model

The Ferrari-Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider $M$ such diffusions conditioned not to intersect. We show that the top process converges to the Airy${}_2$ process as $M\to \mathrm{\infty }$. We then explain the relation with the 3D Ising model and present some conjectures about it.