A central limit theorem for square ice

TL;DR

This paper proves a central limit theorem for the height function in the uniform six-vertex model, showing that after logarithmic rescaling, the height function exhibits Gaussian fluctuations.

Contribution

It establishes a central limit theorem for the height function of the uniform six-vertex model, a significant step in understanding its probabilistic behavior.

Findings

Height function satisfies a central limit theorem after logarithmic rescaling.

Height fluctuations are Gaussian in the scaling limit.

Provides rigorous probabilistic analysis of the six-vertex model.

Abstract

We prove that the height function associated with the uniform six-vertex model (or equivalently, the uniform homomorphism height function from $\mathbb Z^2$ to $\mathbb Z$) satisfies a central limit theorem, upon some logarithmic rescaling.