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 $M\to \infty$. We then explain the relation with the 3D Ising model and present some conjectures about it.

arXiv comment20 pages, LaTeX

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Cited by in corpus (1)

• Uniqueness, mixing, and optimal tails for Brownian line ensembles with geometric area tilt