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arXiv · 2209.14047

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

Patrik L. Ferrari·Senya Shlosman
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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.

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Patrik L. Ferrari, Senya Shlosman. 2022-09-28. The Airy$_2$ process and the 3D Ising model. https://doi.org/10.1088/1751-8121/acb247

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