Dominos and the Gaussian free field

TL;DR

This paper establishes that the scaling limit of the height function in domino tilings converges to the massless free field, a Gaussian process, revealing deep connections between combinatorial models and Gaussian fields.

Contribution

The paper rigorously proves that the height function in domino tilings converges to the massless free field in the scaling limit, linking combinatorics and Gaussian processes.

Findings

Height function converges to the massless free field

Scaling limit is a Gaussian process with independent coefficients

Connects domino tilings to Gaussian free fields

Abstract

We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.