Airy diffusions and $N^{1/3}$ fluctuations in the 2D and 3D Ising models

Consider the 3D Ising model at a low temperature. We will look at the level lines of the Ising droplet near its edge. I will explain that their fluctuations are of the order of $N^{1/3}$. When scaled by $N^{1/3}$, their limiting behavior for large $N$ is given by the Airy diffusion process.
Work in progress with D. Ioffe and Y. Velenik.