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

TL;DR

This paper demonstrates that the top process of multiple non-intersecting Ferrari-Spohn diffusions converges to the Airy$_2$ process as the number of diffusions grows, providing insights into the 3D Ising model's behavior.

Contribution

It establishes the convergence of conditioned Ferrari-Spohn diffusions to the Airy$_2$ process and explores their connection to the 3D Ising model.

Findings

Top process converges to Airy$_2$ as M→∞

Relation between diffusions and 3D Ising model discussed

Conjectures about 3D Ising model presented

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.