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

Abstract

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 → ∞. We then explain the relation with the 3D Ising model and present some conjectures about it.